Spray 2 baking sheets with nonstick spray. Set aside.
Cut off and discard the tough ends of the asparagus stalks. Lay asparagus on the sheets. Lay carrots and pepper strips on the sheets as well.
Cut eggplant lengthwise into six to eight 1/4-inch slices. Blot excess moisture from the slices with paper towels. Arrange the eggplant slices flat on the sheets. Sprinkle veggies with the salt and black pepper.
Roast the veggies until tender, about 15 minutes.
Once the veggies are cool enough to handle, place one basil leaf lengthwise on an eggplant slice. Add a cherry tomato at the short base of the slice. Roll up the eggplant around the tomato and secure with a toothpick. Repeat with all of the other eggplant slices.
If you like, refrigerate the eggplant rolls and roasted veggies until completely chilled, at least 1 hour.
When it's time to serve, arrange the roasted veggies on a platter with the jicama and sugar snap peas.