Are you going to share your secrets with the class?
My guess:
The hard part is turning a spherical hole in the "cheese." Did you steam the mouse or the cheese (or both) before popping the mouse in?
Easier to do, but harder to get right:
Assemble the cheese in two halves with a hidden glue line.
nice try but no cookies for that one !
No you need a flat topped rest to safely turn the hole in the cheese .
So the angled cheese is hot glued to a thick wood face plate at an angle so the front face is flat ( That is very important !). Drill part way in to the cheese with 25mm forstner , go say 25 mm deep , then change drill and drill all the way through with a 10mm drill . That gives you a hole for his tail to poke through.
You then using the flat topped rest AS CLOSE AS YOU CAN to the front face of the cheese and a small
very sharp scraper hollow the cavity to a round shape. Stop frequently to clear shavings as you go. You just need it to be a nice round cavity for your mouses bum to fit in. carefully sand the cavity a bit to finish .
For the mouse you turn a tear drop shaped mouse holding the wood either in a glue chuck or between centres , a chuck is easier as you need a nice pointed nose so once he's in situ no one can grip him to pull him out. This is when you get fanatical with the calipers as his bum must be about 0.5mm bigger than the hole in the cheese you've just made. Mouse is sanded and polished to a high gloss and very smooth( essential ). The cheese is oil finished . Now to fit his ears use a hole punch to make some 8mm diameter leather circles ( old pair of gloves is ideal for the leather ) . drill two holes about 4mm diameter opposite sides of his face , then roll the leather circles apply a little pva into the holes and using a scriber push them home and turn until facing forwards appealingly . Using a sharp marker pen or paintbrush add eyes and nose. Drill a 2mm hole in the round end and apply pva then a thin strip of leather for his tail. let these dry before pushing him home.
To insert him in his hole I use a nylon block now with a drilled recess to fit his nose .Firstly pull his tail through the 10mm hole so people can see he goes all the way in but not how ! I have now found a little touch of oil around the hole rim helpful but not essential. place him in position above the hole.
A sharp tap with a mallet punches him home never to emerge. Originally I used a hide mallet and no block but this tended to squash his nose unless the fit was nearly slack , the nylon block allows a little more force and doesn't mark him.
Hope that's clear enough?
personally I love turning holly, air dried ( splits like anything but it can be done). It turns like butter, holds detail incredibly well and finishes wonderfully to the touch.