Preheat the oven to 425. Toss the zucchini, squash and artichoke hearts with the olive oil on a baking sheet; season with salt and pepper. Roast until tender, about 15 minutes.
Meanwhile, heat the butter in a large deep skillet or Dutch oven over medium-high heat. Add
the garlic, celery, onion and carrot and cook until the vegetables are slightly tender, about 5 minutes. Add the tomatoes and basil, season with salt and pepper and cook until the vegetables are tender, about 8 minutes. Add the vodka and bring to a boil, then reduce to a simmer and cook until slightly thickened, about 1 minute. Puree the sauce with a blender, then add the heavy cream and bring to a boil, stirring occasionally. Season with salt and pepper.
Meanwhile, bring a large pot of salted water to a boil. Add the fusilli and cook as the label directs. Drain and transfer to the skillet with the sauce. Add the roasted vegetables and toss. Garnish with more basil and parmesan.