Heat 1 tablespoon butter in a Dutch oven or ovenproof pot over high heat.
Add the broccolini and stir-fry until just tender, 3 to 4 minutes.
Transfer to a plate using a slotted spoon.
Add the sausage, onion and carrot to the pot and cook, breaking up the meat, until browned, about 5 more minutes.
Add the rice and garlic and cook, stirring, 1 more minute.
Add the wine to the pot and cook until evaporated, about 2 minutes.
Add the chicken broth, tomatoes and 1 cup water; cover and bring to a boil.
Transfer the pot to the oven and bake until the rice is tender, about 15 minutes.
Remove the pot from the oven. (Don't worry if the risotto seems wet; it will thicken when you add the cheese.) Vigorously stir in the remaining 2 tablespoons butter and the cheese until creamy, 1 to 2 minutes. Stir in the broccolini and divide among bowls.