Process ricotta, eggs, 1 teaspoon salt, pepper, and nutmeg in a food processor until smooth. Add flour and blend until a smooth, semi-stiff batter forms. Transfer gnocchi batter to a bowl, cover the bowl with plastic wrap, and refrigerate for 1 hour.
Heat oil in a large saucepan over medium-high heat. Saute mushrooms in hot oil until soft and fragrant, 3 to 5 minutes. Add garlic and saute for 1 minute. Add vegetable broth, bring to a boil and reduce to a simmer; stir in peas. Cook until peas are soft, 3 to 5 minutes. Season with salt and pepper to taste.
Fill a large pot with lightly salted water and bring to a rolling boil.
Working in batches, drop spoonfuls of ricotta batter into boiling water. Bring water back to a boil and cook for 3 minutes. Remove gnocchi to ice water to stop the cooking process, then drain and reserve. Repeat with remaining batter.
Combine gnocchi and mushroom sauce in a saucepan and cook until heated through, 2 to 5 minutes.