Heat the oven to 500°F.
Bring a large pot of salted water to a boil. Cook the pasta until very al dente, about 2 minutes less than package directions. (It will continue softening in the oven). Reserve ~1 cup pasta water, then drain.
Meanwhile, in a large deep sauté pan or braiser, heat the oil over medium heat until shimmering. Add the broccolini, 1/2 teaspoon salt, and several grinds black pepper. Cook until bright green and charred in spots, 3 to 5 minutes. Add the garlic and red pepper flakes and cook, stirring, until fragrant, about 1 minute. Remove from the heat and stir in the beans and drained pasta.
In a mini or standard food processor, combine the cottage cheese, 1/2 cup of the mozzarella, 1/4 cup of the Parmesan, and several grinds black pepper. Process until smooth. Remove half from the food processor and set aside.
Add the marinara sauce to the remaining cheese mixture in the food processor and process until smooth. Pour the creamy sauce into the sauté pan and toss to coat, adding a splash of pasta water as needed until the sauce coats the pasta.
Dollop the reserved cheese mixture on top. Sprinkle with the remaining mozzarella and Parmesan cheeses. Transfer to the oven and bake until brown and bubbly, 10 to 15 minutes. (For an extra browned top, broil for a few additional minutes).
