Bring a large pot of salted water to a boil. Add the pasta and cook as the label directs, adding the broccolini during the last 3 minutes. Reserve 1 cup cooking water, then drain.
Meanwhile, heat the olive oil in a large, deep skillet over medium-high heat. Add the jalapeno and cook, stirring, until softened, about 1 minute. Add the beans, 1/2 teaspoon salt and a few grinds of pepper. Cook, stirring occasionally, until the beans start to crisp, about 3 minutes.
Add the pasta and broccolini to the skillet along with 1/2 cup of the reserved cooking water and the pecorino. Cook, stirring, until the pasta is coated, adding more of the reserved cooking water as needed to loosen; season with salt and pepper. Top each serving with the mozzarella and more grated pecorino; drizzle with olive oil.