Arrange a rack in the top third of the oven and heat the oven to broil on high.

Quarter 1 pound cremini mushrooms. Mince 5 garlic cloves. Strip the leaves off 1 fresh rosemary sprig and coarsely chop. Finely grate 2 ounces Pecorino Romano or Parmesan cheese (about 1 packed cup).

Melt 1 tablespoon of the unsalted butter in a broiler-safe large skillet over medium-high heat. Add the mushrooms and sear, undisturbed, until the bottoms are well-browned, about 3 minutes. Season with ½ teaspoon kosher salt and ¼ teaspoon red pepper flakes, and cook, stirring once or twice, until the mushrooms are browned all over and just tender, about 3 minutes.

Reduce the heat to medium. Cut the remaining 3 tablespoons unsalted butter into 2 pieces and add it to the skillet along with the garlic and rosemary. Sauté until the mixture is saucy and very fragrant, about 2 minutes. Remove from the heat and stir in 1 tablespoon balsamic vinegar. Transfer the mixture to a bowl.

Return the skillet to medium-high heat and heat 1 tablespoon olive oil until shimmering. Add 2 (9 or 10-ounce) packages or 1 (20-ounce) package fresh or frozen cheese ravioli to the skillet, gently breaking apart any that might be stuck together. Sauté until golden brown in spots, 2 to 3 minutes.

Carefully add ½ cup water. Cover and cook until the ravioli is al dente and most of the water is absorbed, 3 to 5 minutes. Uncover and remove from the heat.

Return the mushrooms and their sauce to the skillet. Add a handful of the grated cheese and gently toss to combine. Sprinkle the remaining grated cheese over the top, then broil until the cheese melts and browns in spots, 2 to 3 minutes. Serve garnished with more red pepper flakes, if desired.