Step 1

In a large pot of boiling salted water, cook pasta until al dente according to package instructions, adding kale 2 minutes before end. Reserve 1 cup pasta water; drain. Meanwhile, in a large straight-sided skillet, heat oil, red-pepper flakes, garlic, and tomatoes over medium. Season with salt and cook, stirring, until tomatoes begin to burst, about 10 minutes.

Step 2

Season shrimp with salt and arrange in a single layer on top of tomatoes. Cover and cook until shrimp are bright pink and opaque, about 2 minutes. Remove from heat. Add pasta and kale, butter, and 1/2 cup pasta water; toss until pasta is well coated, adding more pasta water as needed. Serve with cheese and more red-pepper flakes.