Process ricotta, eggs, salt, pepper, and nutmeg in a food processor until smooth. Add flour and blend until a smooth, semi-stiff batter forms. Transfer batter to a bowl, cover with plastic wrap, and refrigerate for 1 hour.

Heat olive 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 boil, then reduce to simmer. Stir in peas and cook until soft, 3 to 5 minutes. Season with salt and pepper.

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. Return water to boil and cook for 3 minutes. Transfer gnocchi to ice water, then drain and reserve.