Preheat the oven to 400 degrees F (200 degrees C).
Whisk eggs, Parmesan cheese, half and half, ricotta, pesto, thyme, salt, and pepper together in a large bowl.
Place vegetables in a microwave-safe bowl; cook on High in the microwave until thawed, 4 to 5 minutes. Drain well.
Melt butter in an ovenproof nonstick skillet. Add garlic and saute until fragrant, about 1 minute. Add steamed vegetables, and toss to coat.
Pour half of egg mixture into the skillet. Toss cooked spaghetti with remaining egg mixture. Pour egg-coated pasta into the skillet. Cook 5 minutes.
Bake in the skillet in the preheated oven until eggs are firm, about 25 minutes. Remove, cut into wedges, and serve with more pesto if desired.
