Combine mayonnaise, fresh basil leaves, lemon juice, minced garlic, salt, and black pepper in a small food processor or blender. Pulse until smooth and evenly green, scraping down the sides as needed. Taste and adjust seasoning. Chill while preparing the rest of the wrap (about 10–15 minutes).

Wrap filling

Prepare and cook bacon

Heat a skillet over medium heat. Add chopped bacon pieces in a single layer and cook, stirring occasionally, until crisp, about 6–8 minutes. Use a slotted spoon to transfer bacon to a plate lined with paper towels to drain. Reserve about 1 teaspoon of bacon fat in the pan and discard the rest or save for another use.

Season and cook chicken

Pat chicken breasts dry, then season both sides with 1 tsp salt and 1/2 tsp black pepper. Heat 1 tablespoon olive oil in the same skillet over medium-high heat. Add chicken breasts and cook 5–7 minutes per side, until golden and an instant-read thermometer inserted into the thickest part reads 165°F (74°C). Remove chicken to a cutting board and let rest 5 minutes, then slice thinly or shred with two forks.

Prepare produce

While chicken rests, core and thinly slice the tomato. Halve the avocado, remove the pit, scoop out the flesh and slice or mash slightly with a fork (season avocado with a pinch of salt if desired). Rinse and dry the shredded romaine lettuce.

Assembly

Warm tortillas (optional)

Warm the flour tortillas in a dry skillet over medium heat 15–20 seconds per side or wrap in foil and heat in a 300°F (150°C) oven for 5–7 minutes. For extra flavor, brush lightly with butter or oil before warming.

Assemble wraps

Lay one warm tortilla flat. Spread about 1 to 1 1/2 tablespoons of basil mayonnaise down the center of the tortilla. Layer 1/2 cup shredded lettuce, a few slices of tomato (about 2–3 slices), 1/4 of the cooked sliced chicken (about 1/2 chicken breast), 1/4 of the cooked bacon (about 1-2 slices worth of chopped bacon), and 1/4 of the sliced or mashed avocado. If you like, add extra drizzle of basil mayo on top.

Roll and serve

Fold the bottom edge of the tortilla up over the filling, fold in the sides, and roll tightly to close. Repeat for remaining tortillas. Cut each wrap in half on a diagonal and serve immediately. Optionally secure with a toothpick. Serve with extra basil mayo on the side.