Special equipment: Toothpicks
Pull the largest four romaine leaves from the outside of the bunch and wash and dry carefully, trying not to tear the leaves. Cut the leaves at the base where they were connected to the root; the pieces should be about 9-inches long. Using a vegetable peeler, shave the center rib so the leaves roll up more easily. Set aside.
Combine the cream cheese, spinach and basil in a food processor and puree until smooth. Season with 1/4 teaspoon kosher salt and a few grinds of pepper.
Lay one of the tortillas on a clean work surface and add one of the romaine leaves to fit neatly on top. Place 2 slices of turkey next to each other, covering the lettuce. Spread 2 tablespoons of the cream cheese mixture over the surface of the turkey and line up a quarter of the roasted pepper strips along one edge. Line up 1/4 cup of the shredded carrot just above the peppers. Roll up the wrap tightly starting from the edge with the peppers and carrots, so the wrap holds together with the peppers and carrots in the middle. Place the wrap seam-side down. Repeat with the remaining tortillas, vegetables, turkey and cream cheese spread. Cut the wraps into 1-inch pieces, then pierce each segment with a toothpick or skewer from the outside of the tortilla through the seam on the bottom.
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