Prepare the grill for direct and indirect cooking over medium heat (350° to 450°F).
Brush the cooking grates clean. Grill the sausages over direct medium heat, with the lid closed, until browned and warmed through, 10 to 12 minutes, turning as needed. Transfer to a cutting board. Brush the broccolini with oil and lightly season with salt. Arrange the stalks perpendicular to the cooking grates over direct medium heat. Grill, with the lid closed, until the broccolini is lightly charred and crisp-tender, 3 to 4 minutes, turning once. Transfer to a cutting board. When cool enough to handle, cut the sausages into 1/2 inch slices, and cut the broccolini into bite-sized pieces.
Preheat a large-cast iron skillet for 10 minutes over direct medium heat.
Add 2 tablespoons oil to the skillet. Add the tomatoes and cook over direct medium heat, with the lid closed, until the tomatoes blister, begin to collapse, and release their juices, 6 to 8 minutes, stirring frequently. Add the garlic, red pepper flakes, and 1/2 teaspoon kosher salt and stir until fragrant, about 30 seconds. Slide the skillet over indirect medium-high heat and keep warm while you cook the pasta.
In a large pot of boiling salted water on the stove, cook the penne according to the package instructions until al dente. Drain the penne and add to the skillet. Remove the skillet from the heat and stir in the sausages with any accumulated juices, the broccolini, cheese, and basil. Garnish with pepper and serve with additional cheese for sprinkling.