Preheat the oven to 400°F and line 2 large baking sheets with parchment paper. Place the carrots and onions on the first sheet and the pattypan squash, zucchini, and tomatoes on the other. Drizzle both sheets of vegetables with olive oil and generous pinches of salt and pepper. Place the sheet with the carrots and onions in the oven first and roast for 30 to 35 minutes or until the onions are tender and lightly charred, and the carrots are tender and browned. Place the second sheet in and roast for 20 minutes, or until the squash and zucchini are golden brown around the edges, and the tomatoes are lightly bursting. Remove from the oven and set aside.
In the bottom of a large bowl, combine the 1 tablespoon of olive oil with the sherry vinegar, garlic, herbes de Provence, thyme, ¼ teaspoon salt, and several grinds of black pepper. Stir in the roasted vegetables.
Prepare the pasta according to the instructions on the package, cooking until al dente. Drain and transfer the cooked pasta to the large bowl with the roasted vegetables and toss to coat.
Add the feta, basil, lemon juice, and red pepper flakes and gently toss. Season (generously!) to taste with more salt, pepper, and lemon juice, as desired.
Garnish with more fresh herbs and a generous drizzle of olive oil.