Bring a large pot of salted water to a boil for the ravioli.
Warm olive oil and 1 tbsp butter in a wide skillet over medium-high heat.
Add sliced mushrooms; cook undisturbed 3 minutes, then stir and sauté until browned, 4–5 minutes more.
Reduce heat to medium. Melt in remaining 1 tbsp butter, then stir in shallot and garlic; cook until fragrant, about 1 minute.
Season with thyme, sage, red pepper flakes, salt, and black pepper; stir to coat the mushrooms.
Pour in white wine to deglaze, scraping up browned bits; simmer until mostly reduced, 1–2 minutes.
Add broth and bring to a gentle simmer. Stir in heavy cream and cook until slightly thickened, 3–4 minutes.
Boil ravioli according to package directions until they float and are tender; reserve 1/2 cup pasta water, then drain.
Off heat, stir Parmesan and lemon juice into the sauce. Loosen with a splash of pasta water if needed.
Gently fold ravioli into the sauce. Sprinkle with parsley and extra Parmesan; serve immediately.