Place racks in bottom third and middle of oven; preheat to 350°F. Toss mushrooms, garlic, thyme, red pepper flakes, 1/4 cup oil, and 1/2 tsp. salt on a rimmed baking sheet. Roast on bottom rack, tossing halfway through, until deeply golden brown and crisped, 25–30 minutes.

Heat 2 Tbsp. oil in a large ovenproof Dutch oven or heavy pot over medium-high. Add onion and cook, stirring often, until softened and slightly translucent, 3–5 minutes. Stir in rice; season with pepper and 1/2 tsp. salt. Cook, stirring occasionally, until some grains are translucent, about 2 minutes. Add vermouth, bring to a simmer, and cook, stirring occasionally, until pan is almost dry, about 2 minutes. Add 2 1/2 cups stock. Bring to a simmer, then cover and bake in oven until liquid is mostly absorbed but rice is still slightly firm in the center, 16–18 minutes.

Return pot to stove and heat over medium. Add remaining 1/2 cup stock and cook, stirring constantly, until rice is tender but still has some bite and sauce is creamy, about 2 minutes. Remove from heat and stir in Parmesan, butter, and lemon zest; season to taste with salt, if needed. Add a little bit of warm water, if needed, until risotto is thick but still pourable.

Transfer risotto to a platter. Top with crispy mushrooms and parsley. Drizzle with oil. Serve with lemon wedges alongside.