Pasta with Anchovy Butter and Broccoli Rabe

Mash anchovies into butter in a medium bowl; season with salt (if needed; taste first) and pepper. Tear broccoli rabe leaves into 2" pieces; set aside. Thinly slice stems 1/4" thick. Heat oil in a large skillet over medium. Add garlic and broccoli rabe stems and season with salt and pepper. Cook, stirring occasionally, until stems are tender, about 5 minutes. Meanwhile, cook pasta in a large pot of boiling salted water, stirring occasionally, until al dente. Drain, reserving 1/2 cup pasta cooking liquid. Add pasta, reserved broccoli rabe leaves, 1/4 cup pasta liquid, and 3 tablespoons anchovy butter to skillet (save remaining butter for another use). Cook, tossing occasionally and adding more pasta liquid as needed, until leaves are wilted and sauce coats pasta, about 4 minutes. Toss in grated Pecorino; season with salt and pepper. Serve pasta topped with shaved Pecorino.