Preheat oven to 350 degrees. Heat oil in a 9-or 10-inch ovenproof nonstick skillet over medium heat until hot but not smoking. Add mushrooms, onion, and thyme; cook, stirring, until mushrooms and onion are golden brown, about 10 minutes. Stir in 1/2 teaspoon salt; remove skillet from heat.
Whisk eggs in a large bowl until frothy. Stir in the ricotta, 1 teaspoon salt, and pepper to taste. Place reserved skillet over medium heat. Immediately pour in egg mixture, and lightly stir to distribute mushrooms and onion evenly. Reduce heat to medium-low; cook 2 minutes, drawing cooked egg away from sides with a rubber spatula to let uncooked egg flow underneath. Cook until just starting to set, about 2 minutes more.
Transfer skillet to oven. Bake until frittata is just set and top is pale golden, 10 to 12 minutes. Serve frittata in skillet, or slide onto a serving platter.
For a frittata that's lower in cholesterol, make this recipe using seven whole eggs and three egg whites. The cholesterol per serving will be 258 milligrams. If you prefer, use 10 egg whites (no yolks), which reduces the cholesterol per serving to just 11 milligrams. Per serving: 230 calories, 16 g fat, 365 mg cholesterol, 9 g carbohydrate, 408 mg sodium, 14 g protein, 2 g fiber