Arrange chicken, skin side up, in a single layer in a shallow dish. Combine soy sauce, mirin, sugar, garlic, and ginger; pour over chicken. Marinate in refrigerator, turning once or twice, for 30 minutes to 1 hour. Heat grill. Remove chicken from marinade. Place on grill, and cook, basting with marinade, about 12 to 15 minutes, turning once. Let cool and slice in thin strips.
Dress the romaine and julienne vegetables with the aioli and place on the bottom 1/3 of the tortilla. Top with the sliced chicken and the pineapple. Fold over the edges and snuggly roll up your burrito, dig in and smile!
Place the yolks, juice, vinegar, soy sauce, ginger, garlic, and chile powder in a blender on medium speed. While blending, drizzle in the vegetable oil and then the sesame oil. Season, to taste, with the salt.