Whisk the mayonnaise, lemon juice, nutritional yeast, Dijon mustard, Worcestershire sauce, anchovy paste, garlic, pepper, and water until smooth and creamy.
Slice the chicken breasts in half horizontally and season with garlic powder, Italian seasoning, salt, and pepper. Cook in the olive oil in a large skillet over medium-high heat for 5-6 minutes per side until golden and 165°F, then rest for 5 minutes and slice.
In a large bowl, toss the romaine and crushed croutons with about three quarters of the dressing until evenly coated.
Warm the tortillas in a dry skillet for 15-20 seconds per side so they fold without cracking.
Fill the center of each tortilla with Caesar salad and sliced chicken, then drizzle with the remaining dressing. Fold in the sides and roll up tightly.
Place the wraps seam side down in the skillet over medium heat and toast for 1-2 minutes per side until golden and sealed. Slice in half and serve.