Place racks in bottom third and middle of oven; preheat to 350°F/180C. 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.
Meanwhile, heat 2 tbs 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 a 350F/180C 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.