Oven Risotto with Mushrooms

Ingredients

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