Heat the oil in a 10-inch regular or cast iron skillet over medium-high heat. Add the sausage and cook until evenly browned on both sides, 3 to 4 minutes. Add the broccolini, season with salt and pepper, and sauté until vibrant green and almost tender, about 5 minutes. Add the garlic and orzo and sauté until fragrant, about 1 minute.

Add the chicken broth and bring the mixture to a boil. Cover, reduce to a simmer, and cook until the pasta is al dente and the liquid is absorbed, about 10 minutes or according to your orzo's package instructions. Stir in the ½ cup of Parmesan and season as needed with salt and pepper. Garnish with additional grated cheese if desired.