Preheat oven to 425°F. Toss vegetables on a sheet pan with olive oil, salt and pepper. Roast for 15 minutes, stir, and continue roasting until browned and tender, 10 to 15 minutes.
Meanwhile in a small bowl, mix pesto with mayonnaise until combined. Spread evenly onto wrap, leaving about a 1-inch border around the edges of wrap.
Arrange one fourth of the roasted vegetables in the middle of each wrap, top with one fourth of the feta cheese, and a handful of spinach. Wrap tightly. Repeat with remaining wraps. Enjoy immediately.
