Bring a large pot of salted water to a boil and cook the pasta to 1 minute under al dente (you'll finish cooking it in the pan). Drain, reserving 1 cup pasta water.

Meanwhile, in a large skillet over medium-high heat, melt 2 tablespoons butter. Add the mushrooms in a single layer, season with salt and pepper, and cook for 5–6 minutes without stirring until they're golden on one side. Toss, then cook another 3–4 minutes until tender. Transfer to a plate.

Reduce heat to medium. Add the remaining 2 tablespoons butter to the skillet. Mince the garlic and sauté for 30 seconds until fragrant. Pour in the wine and scrape up any browned bits from the pan. Simmer for 1 minute.

Add the broth, thyme, and reserved pasta. Stir and simmer for 2–3 minutes, adding pasta water a splash at a time, until the sauce is silky and the pasta is tender. The starch from the pasta will help thicken it.

Return the mushrooms to the pan. Squeeze the juice from the lemon over everything. Taste and adjust salt and pepper. Discard thyme sprigs.

Divide between bowls. Grate or shave parmesan over each serving and serve immediately.