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. (If the pasta is cooked before the liquid is completely absorbed, uncover the skillet and let it simmer for an extra minute to evaporate it.) Stir in the 1/2 cup of Parmesan and season as needed with salt and pepper. Garnish with additional grated cheese if desired.