Following the same instructions as the Fresh Pasta Tutorial, make pasta dough (make a well in the center of the flour, add the egg, oil, water, and salt and combine). Store in an airtight container for 30 minutes to rest.
Mince garlic and shallots. Rough chop the mushrooms.
Add garlic and shallots to a hot pan with butter, olive oil, and salt. Cook until slightly translucent. Add mushrooms, pepper, and thyme. Cook down until mushrooms are soft and water has cooked out.
Add red wine and cook down until it is reduced by half. Your pan should be mostly dry at this point.
Add mushroom mixture, parmesan, and ricotta to a food processor and blend until a pate is formed. Taste and add salt & pepper to your liking.
Roll pasta out into thin sheets. You should be able to read through them. I usually split this dough into two sections to roll. If using a Kitchen Aid, roll to setting 7.
Following the instructions in the post, spoon a teaspoon of mushroom mixture into the middle of the dough sheets approx. 1.5" apart. Fold the dough over, and using a cookie cutter or mason jar lid cut the dough into a half moon shape.
Set the mezzelune on a floured cookie sheet or floured surface until ready to cook.
Make the sauce.
In a hot pan, sauté garlic in olive oil and butter until slightly brown. Do not burn the garlic.
Whisk in the heavy cream and simmer until it begins to thicken. Whisk in the parmesan, pepper, and thyme. Turn heat on low and keep warm.
Meanwhile, boil water for the pasta. These mezzelune will cook quickly (like, 3 minutes or less). Once they are cooked add them straight to the sauce.
Portion onto a plate and serve with fresh grated parmesan!