Step 1

Arrange 2 racks to divide the oven into thirds and heat to 400°F.

Step 2

Toss the sweet potatoes with 3 tablespoons of the oil and 1 teaspoon kosher salt. Arrange in a single layer on 2 rimmed baking sheets. Roast until the potatoes are tender and browned around the edges, about 35 minutes total, stirring halfway through. Cool for about 5 minutes, then transfer the sweet potatoes to a large plate, reserving the baking sheets.

Step 3

Toss the mushrooms with 1 1/2 tablespoons of oil and 1/2 teaspoon of salt. Place in a single layer on a rimmed baking sheet. Toss the tomatoes with 1/2 tablespoon oil and arrange cut-side up on the second rimmed baking sheet. Roast for 15 minutes, stirring the mushrooms once about halfway through. Cool on the baking sheets.

Step 4

Meanwhile, caramelize the onions. Heat the remaining 1 1/2 tablespoons oil in a large skillet over low heat until shimmering. Add the onions and 1/2 teaspoon salt. Cook, stirring every 5 to 10 minutes, until the onions are soft and deeply browned, scraping any fond from the bottom of the pan, about 40 minutes total. Add the water to deglaze the pan and allow the moisture to cook off.

Step 5

Assemble the wraps: Place the tortillas on a work surface. Spread 1 tablespoon of pesto on a tortilla. Add 1/2 cup of sweet potato over the tortilla, just below center. Top the sweet potatoes evenly with a couple mushroom slices, and a tablespoon each of caramelized onions, tomatoes, and Parmesan cheese. Roll tightly by folding the sides over the filling, then rolling from the bottom up. Repeat with assembling the remaining wraps.

Step 6

Reheating: If not serving immediately, cover each wrap tightly in foil. Refrigerate or freeze in resealable plastic bags. Reheat in a regular or toaster oven at 350°F, wrapped in foil for first 10 minutes and unwrapped for the final 5, if frozen.