For the sauce: Combine all ingredients in a blender and process until smooth; set aside until ready to use. If the sauce is too thick, add a little more water. (Can be made up to 1 day ahead and stored, covered tightly in a refrigerator until ready to use.)
For the turkey: Combine flour, zest, salt, and pepper in a shallow dish or a resealable plastic bag and mix thoroughly. Add half of cutlets and coat well. Remove, shaking off excess flour, and repeat with remaining cutlets.
Heat 1 tablespoon oil in a large frying pan over medium heat. When it shimmers, add 2 to 3 cutlets and cook until browned, about 3 minutes total. Transfer to a plate and repeat with remaining cutlets.
To serve, place turkey on platter, top with sauce, and garnish with a few slices of avocado and torn basil leaves.