Cook the pasta in plenty of rapidly simmering water until al dente, then drain.
Meanwhile, heat 1 tablespoon of the oil in an extra-large skillet or steep-sided stir-fry pan. Add the onion and sauté over medium heat until translucent.
Add the garlic and continue to sauté until the onion is golden.
Add the wine and cauliflower and cook, covered, for 3 minutes.
Stir in the broccoli, asparagus, squash, and canned tomatoes, and dried herbs. Bring to a simmer, then cover and cook over medium heat for 5 to 7 minutes, or until all the vegetables are tender-crisp.
When the pasta is done, drain it well and combine with the vegetables mixture right in the pan, if it's large enough, or in a large serving bowl. Add the remaining 2 tablespoons of olive oil unless you used oil-packed sun-dried tomatoes, in which case add a bit more of their oil if you'd like.
Stir in as much basil as you'd like, and season to taste with salt and pepper. Add dried hot red pepper flakes if using them.
Serve at once. If desired, pass around some vegan Parmesan cheese for topping each serving.