Oven Risotto with Mushrooms

Name: Oven Risotto with Mushrooms
Cuisine: Italian
Ingredients: 1 lb. mixed wild, shiitake, and/or crimini mushrooms, broken into pieces or sliced ¼" thick (about 4 cups); 3 garlic cloves, peeled, thinly sliced; 6 thyme sprigs; ¼ tsp. crushed red pepper flakes; ¼ cup plus 2 Tbsp. extra-virgin olive oil, plus more for drizzling; 1¾ tsp. (or more) kosher salt, divided; 1 medium onion, finely chopped; 1 cup arborio rice; ½ tsp. freshly ground black pepper; ½ cup dry vermouth or white wine; 3 cups homemade chicken stock or low-sodium chicken broth, divided; 2 oz. finely grated Parmesan (about 1 cup); 2 Tbsp. cold unsalted butter, cut into pieces; ½ tsp. finely grated lemon zest; ⅓ cup coarsely chopped parsley leaves; Lemon wedges (for serving)