Heat the oven to 425°F. Line a large rimmed sheet pan with parchment for easy cleanup. Prep the vegetables and aromatics, slice the sausages, and zest and juice the lemon.
On the sheet pan, toss the sausage, zucchini, tomatoes, and shallot with 2 tbsp olive oil, kosher salt, black pepper, garlic powder, Italian seasoning, red pepper flakes, balsamic vinegar (if using), and half of the minced garlic. Spread in an even layer.
Roast for 12 minutes, stir, then roast 4 to 6 minutes more, until the zucchini is tender and the edges of the sausage are browned. For deeper color, broil 1 minute at the end while watching closely.
Meanwhile, boil the pasta in well-salted water until just al dente. Reserve about 3/4 cup pasta water, then drain.
Return the empty pot to medium heat. Add the remaining 1 tbsp olive oil and the butter. When the butter foams, add the remaining minced garlic and cook 30 seconds, just until fragrant. Stir in 1/2 cup reserved pasta water, the lemon zest, and 2 tbsp lemon juice; simmer 1 minute to emulsify.
Take the pot off the heat and add the drained pasta and 1 cup of the Parmesan. Toss until glossy, adding a splash more pasta water as needed so the sauce clings to the noodles.
Fold in the roasted sausage and vegetables along with any pan juices. Taste and adjust with more salt, pepper, or lemon juice to balance.
Transfer to a 9×13-inch baking dish and sprinkle with the remaining 1/2 cup Parmesan. Bake at 425°F for 5 to 7 minutes, until the cheese melts and the top is lightly golden. Garnish with basil and cracked black pepper. Serve hot with lemon wedges.