But what'll happen to the cheese down in the mantle, with the massive weight of hundreds of kilometers of cheese crushing it? It will quickly separate into water and casein, with the water rising up towards the surface and the denser casein being forced further downwards. The protein will almost immediately start to break down into simpler products like water, NH3, and carbon. If you add up the amino acids that make casein, you see that the bulk composition is something like C6 H11 O4 N. The most stable set of end-products would probably be 8H2O + C2H6 + N2 + 10C. I get that we start with about 2x10^24 moles of water plus about 2x10^23 "moles" of casein, and end up with:
1x10^24 moles of C --> 8x10^22g --> 100 km radius core 3x10^24 moles of water --> 2x10^23g --> 400 km deep oceans 2x10^23 moles of ethane --> 1x10^22g thick atmosphere 1x10^23 moles of N2 --> 4x10^21g " "
So unless I've made a big math mistake somewhere, the green cheese Moon would quickly evolve into a strange little Europa-like or Titan- like world, with a very dense graphite core, a thick atmosphere and deep oceans, and almost no leftover cheese.