Create a flour mound on a clean surface, make a well in the center, and add eggs. Incorporate flour gradually, then knead for 10 minutes until smooth. Wrap in plastic and rest for 30 minutes.
Sauté minced mushrooms and half of the garlic in olive oil over medium-high heat until all moisture has evaporated. Allow to cool completely.
In a bowl, combine cooled mushrooms, ricotta, half of the Parmesan, nutmeg, salt, and pepper.
Roll pasta dough into thin sheets using a pasta machine to the thinnest or second-to-thinnest setting.
Place 1-teaspoon mounds of filling 2 inches apart on one pasta sheet. Top with a second sheet, press to remove air, and seal edges. Cut into squares using a pasta wheel.
Bring a large pot of salted water to a boil. Cook ravioli for 3 to 4 minutes or until they float to the surface.
In a large skillet, melt butter over medium heat. Add remaining garlic and sauté for 1 minute until fragrant.
Add fresh spinach to the skillet and toss until just wilted.
Transfer cooked ravioli directly to the skillet using a slotted spoon. Toss gently to coat with butter and spinach.
Serve immediately topped with remaining Parmesan cheese.