Ah so, only 2 ¾” square, huh?
With the metal box being 2 ¾” square infers to me that it is probably a “filled” or “layered” cookie or food press (cutter).
And the way I envision it could have been used:
Roll-out two (2) large layers of dough (like making 2 pie crusts).
Spread the “filling” of choice on one (1) layer … then cover it with the other.
Use the metal box as the “cutter” of the dough …. and the wood “plunger” to “seal” opposites sides of the food “item” and then it could be baked, boiled or whatever.
It would resemble a Fig Newton but with a Ravioli type “concave” crimp on opposite sides.