Pour flour onto a flat surface. Create a well in the middle of the flour and add remaining ingredients. Using a fork, incorporate the outer walls of flour into the wet ingredients until mixed together. Add small amounts of water if too dry. Knead the dough for five minutes; wrap in plastic and rest at least 30 minutes.
Combine mushrooms, cheese, salt, and pepper; reserve.
Using a pasta maker, create two long sheets of dough. Place one teaspoon of filling two inches apart. Cover with second sheet of pasta and press down in intervals to secure filling on all four sides of pasta. Cut between each section of filling. Form each square as desired (twist ends together and press or cook as is).
Boil fresh pasta for three minutes, being sure not to crowd the pot. Remove and carefully drain once pieces rise to the top.
Extra pasta can be frozen, but be sure to boil for up to five minutes if preparing this way.
To serve: lightly toss with olive oil and arrange with prosciutto and sage leaves.