Trim and discard any grit or soil and discolored stem ends from mushrooms (trim and discard shiitake stems). Immerse mushrooms in cool water, swishing gently to rinse well, then quickly lift out and drain. Thinly slice mushrooms.
In a 3- to 4-quart pan over medium-high heat, combine oil, garlic, onion, and mushrooms. Stir often until vegetables just begin to brown, about 6 minutes. Add rice and stir until some of the grains are opaque, about 2 minutes.
Add 4 cups broth to pan; when it boils, reduce heat to medium or medium-low and simmer, stirring often, until rice is just tender to bite, 15 to 20 minutes. Add peas and butter and stir often until peas are tender to bite, 2 to 5 minutes. For a creamier risotto, add more broth until mixture is desired consistency and boiling. Stir in half the cheese. Season risotto to taste with salt and pepper, pour into a bowl, and sprinkle with remaining cheese.