2. Mix the olive oil, garlic, salt, pepper and 1/2 teaspoon of the basil together. Remove the stems from the mushrooms and brush both sides of the caps with the olive oil mixture. Set aside.
3. Grill the mushrooms until they are soft in the center, about 3 to 4 minutes on each side. Slice each cap on the diagonal into 1" strips, and let cool.
For the wraps: 4. Mix the cheese, the remaining 1/2 teaspoon of basil, salt and pepper together. Set aside.
5. Lay the tortillas out and spread 2 tablespoons of the cream cheese mixture on each of them. Place one slice of roasted red pepper on each tortilla and divide the mushroom strips between the tortillas. Tightly roll each tortilla into a cylinder, ending with the seam side down.
(The wraps can be stored in the refrigerator for up to 3 days.)
6. Cut the wraps in half on the diagonal and serve.