Bring a large pot of generously salted water to a boil. Cook the cavatelli according to package directions until al dente. Reserve 1 cup of pasta water, then drain the pasta.

While the pasta cooks, bring a separate medium pot of salted water to a boil. Add the broccoli rabe and blanch for 2 minutes. Drain and immediately plunge into an ice water bath to stop cooking. Drain again and set aside.

In a large, deep skillet over medium-high heat, cook the sausage, breaking it into crumbles, until browned and cooked through to an internal temperature of 160°F (71°C) with no pink remaining, about 6-8 minutes. Use a slotted spoon to transfer the sausage to a plate, leaving 1-2 tablespoons of fat in the pan.

Reduce the heat to medium. Add the sliced garlic and red pepper flakes to the skillet. Cook until fragrant, about 30 seconds. Add the blanched broccoli rabe and sauté for 3-4 minutes, until tender and slightly charred in spots.

Pour in the white wine, scraping up any browned bits. Let it reduce by half, about 1 minute. Return the sausage to the pan, add the butter, and stir. Add the cooked cavatelli and 1/2 cup of reserved pasta water. Toss vigorously over medium heat until the sauce clings to the pasta, adding more water if needed.

Remove from heat, stir in the grated Pecorino Romano, and season with salt and black pepper to taste. Transfer to a serving bowl, drizzle with extra virgin olive oil, and pass additional cheese at the table.