Cook the pasta according to the package directions. Drain and return it to the pot.
Heat the oil in a large skillet over medium-high heat. Add the sausage and cook, breaking it up with a spoon, until browned, 7 to 8 minutes; transfer to a plate.
Add the broccolini to the drippings in the skillet and cook, stirring occasionally, until tender, 5 to 7 minutes (add a little water if the skillet becomes too dark). Stir in the rosemary and red pepper flakes. Add the sausage, broccolini, and bocconcini to the pasta and toss to combine.