Cook pasta in boiling salt water, as instructed on packet. While pasta is cooking, proceed to following.
Heat oil in a deep pan or casserole pan.
Add chopped onions and saute until fragrant and translucent.
Add sliced mushrooms, and cook until soft. Season with a bit of salt and pepper.
Pour in the goat's milk at medium heat, and cook until thickened. Lower heat.
Stir in chopped thyme (fresh or dried).
Remove from heat and set aside until pasta is done.
When pasta is done, strain, and add to mushroom goat's milk sauce on low heat.
Stir gently so as to not break the Paccheri.
Remove from heat, and stir in a teaspoon or more of grated Parmigiano-Reggiano cheese.
Serve immediately.