Mix ricotta, spinach, garlic, salt, red pepper flakes, if using, pepper, 1 1/2 cups mozzarella, and 1/4 cup Parmesan in a large bowl.
Spread 1/2 cup marinara evenly in bottom of baking dish. Top with 2 lasagna noodles. Coat noodles with 1/2 cup marinara. Top with half of the ricotta mixture and half of the mushrooms. Repeat with 2 noodles, 1/2 cup marinara, and remaining ricotta mixture and mushrooms.
Top with remaining 2 noodles, sauce, and 3/4 cup mozzarella. Sprinkle with 2 Tbsp. Parmesan.
Cover dish with parchment, then cover again with an overturned large microwave-safe plate. Microwave on high 15 minutes. Carefully check to see if noodles are tender; if not, re-cover and microwave in 1-minute bursts until tender.
Let stand, covered, 10 minutes. Very carefully remove parchment. Sprinkle with parsley and remaining 2 Tbsp. Parmesan and serve.