Cook the pasta according to the package instructions. Drain and set aside, reserving the water.
Meanwhile, heat the olive oil in a large skillet over medium-high heat until hot, then pinch off 1- to 2-inch pieces of the sausage, adding it to the pan as you go. Cook for a couple minutes, flipping and stirring the sausage to brown both sides. Add the onion and garlic and cook until the onion has softened a little, a couple of minutes. Add the red pepper flakes, salt and pepper. Stir and cook until the sausage is cooked through, another 1 to 2 minutes.
Use a ladle to remove 2/3 cup pasta water from the pasta pot and add it to the skillet. Add the kale and cook until it has started to wilt, about 30 seconds, then add the pesto and cherry tomatoes and cook, stirring gently, until the sauce has thickened and the kale has wilted, about 3 minutes. If the skillet starts to look too dry at any stage, add a little more pasta water.
Remove the skillet from the heat and add the butter, lemon zest, pasta and Parmesan. Toss to combine. Taste and adjust the seasoning, then serve in bowls garnished with the fresh basil.