English is a highly indirect language when it comes to these sorts of statements. "Have you seen the cutting board?" Would indicate that it's not where it should be. "Where is the cutting board" would be too much of a personal accusation. It's the type of thing you would say to a child that had hidden it. "Where do you keep the cutting board" would be how you ask when you honestly don't know, like if you're helping a friend prepare dinner.

"It looks like the second cutting board has grown legs. Any ideas?"

The first sentence uses a sarcastic metaphor that indicates the correct placement is known but the item is not to be found there

The second sentence expresses an interest in knowing what others can tell the speaker about this situation - maybe not quite discontent, but definitely interest in it being located

Something is oddly off and I’m expressing emotional state of curiosity and/or mild discontent: “So …”

It is not where it should be, but I do indeed know where the place it should be is: reference to its place.

Here’s your equivalent question in English:

So … the cutting board’s not in its place. Anybody know where it is?

"Where has the second cutting board gone?"

This indicates that it's not where it's supposed to be, or at least not where you expected it to be and you're looking for it. I can't say for sure as I don't speak German, but in English the "emotional state" you refer to is pretty clear in the context.

“Where is actually our second big cuttingboard thither?"

I lol'd

"Eigentlich" here would be "by the way" because it's used to express curiosity in a marginalised way. "wo ist... hin" is "where has... gone (to)"

So a more literal translation including the undertones would be "By the way, where has our big cutting board gone?"

I think the most direct translation in this context would be "Where on earth is..." (or more extreme) "Where the hell is..."

These inserts add almost exactly the same connotations you describe for "eigentlich", though perhaps also with the implication that you have spent some time looking for it already

O cutting board, cutting board, wherefore art thou cutting board?

Spoken verbally, intonation can get you there. You can imagine this question asked perfectly calmly and innocently, "Where's the cutting board?" "Oh it's over there on the kitchen table." "Ah." Or you could imagine Batman growl screaming it in the Joker's face. WHERE'S THE CUTTING BOARD?!?! TELL ME!!!

Now, in terms of phrasing, "Does anyone know where the cutting board is?" is probably fairly calm and innocent, "Who hid the cutting board?" is more accusatory/conspiratorial, "where'd the cutting board go?" implies you know where it was/should be, but it is not there, "What happened to the cutting board?" might mean it's gone, or it might mean it's damaged or in some adverse state, "Where the hell is the cutting board?" is probably getting a bit angry, "If I were a cutting board, where would I be?" means you're either in a new kitchen and don't know where the tools are stored, or it has been misplaced and you're still calm about it...there are lots of options.

"Where has it gone?" = avoiding assigning blame. "Where did you put it?" = assigning blame.

Add an expletive. Example “where’s the fucking cutting board?”

'Where has the cutting board wandered off to?' Something passively accusatory. Everyone knows the board didn't move itself, but the speaker is not assigning blame. ...and because everyone knows that there is blame to be assigned, the annoyance is sort of implied?

Add a fuck or two.

Where the fuck is the fucking cutting board?

Where the fuck have you fucking little fucker taken the fucking cutting board?

Y'all motherfuckers better tell me where in the fuck you little fucking thief's have taken the fucking cutting board,

The relative size doesn't matter. The fact that the cutting board isn't in the approximate location is should be does. Adding in a bunch of cuss' will express how seriously concerned you are. Get a little more personal and offensive with the cussing will probably speed up the answers, but also get them to hate you more. So use that sparingly.

But general cussing isn't overall too damaging.

Looks like the cutting board didn’t get put away last time it was used, does anyone know where it ended up?

Are you asking how to express this information in a utilitarian way, as in, how do you convey the information to be understood? Or are you asking how to express it in a poetic way? The use of thither makes me think you're hoping to express this is a jokingly poetic sense.

Who has stolen my second big cutting board?

"Who's nicked the cutting board?" Indicates that it is not in its proper place and makes a (light-hearted) accusation of theft to indicate that it shouldn't be anywhere else.

Maybe "Does anyone know where the second big cutting board is?"

Who bloody hell stole the damn cutting board?

As others have mentioned, cursing is is a wonderful way of expressing emotions

Garfield's 1978 pipe strip resonates with a new generation once more!

wunden? Haha just Scheißing