Bring a large pot of salted water to a boil over medium high heat. Cook the pasta until al dente, about 8 minutes. Drain and set aside.
Brush the vegetables with the remaining olive oil. Season to taste with salt and pepper. Heat a grill or grill pan over medium-high heat. Grill until the vegetables are tender and have grill marks, about 5 minutes.
Remove to a cutting board and cool. Cut the zucchini, yellow squash and eggplant into slices.
In a small mixing bowl whisk the mayonnaise, red wine vinegar, balsamic vinegar, lemon juice and garlic together.
Then add the mayonnaise sauce, roasted vegetables, oregano, basil and red pepper then toss so all ingredients are combined.
Add the chevére and toss once more then season to taste with salt and pepper. Serve chilled or at room temperature.