Bring regular and low-sodium vegetable broth to a slow boil in a medium pot over medium heat. Reduce heat slightly and keep warm.

Heat olive oil and 1 tablespoon butter in a 12-inch skillet over medium heat. Add onion, garlic, pepper flakes, and a pinch of salt and pepper. Cook, stirring often, for 3 to 4 minutes.

Add cremini and shiitake mushrooms, fresh and dried thyme, and a generous pinch of salt and pepper. Cook and stir until mushrooms have released their liquid and caramelized a bit, about 5 minutes. Transfer vegetables to a plate and set aside.

Add remaining 1 tablespoon butter to the skillet and return to the heat to melt. Add Arborio rice and stir until rice gives off a toasty smell and appears a little paler in color, about 2 minutes. Add bay leaf, pour in wine, and stir until liquid is absorbed, about 3 minutes.

Use a ladle to scoop some hot broth into the skillet. Cook and stir until all liquid is absorbed, 2 to 3 minutes, before adding another ladle of broth. Continue this process until risotto is just about finished, about 15 minutes. With the final ladle of broth, add frozen peas and return cooked vegetables to the pan.

Remove from the heat once the liquid is absorbed and the rice is tender, yet firm to the bite. Stir in Pecorino Romano cheese and parsley. Taste and adjust salt and pepper if needed.