Place the onion, zucchini, eggplant, mushrooms, and bell pepper into a large container with a tight fitting lid. Drizzle the olive oil over the vegetables and season with salt and pepper. Close the lid and shake to coat.
Heat a grill pan or skillet over medium heat. Place the seasoned vegetables on the preheated pan, stir and cook until tender, about 10 minutes.
Spread each tortilla with 1 tablespoon goat cheese and 1 tablespoon pesto. Divide the sliced avocado among the tortillas and top with the mixed veggies. Fold in the bottom of each tortilla and roll each up into a snug wrap.