Gather all ingredients and have tortillas warmed according to package directions when ready to assemble.
Heat the olive oil in a cast-iron grill pan over medium heat. Toss the chicken pieces with the taco seasoning, add them to the pan, and cook until browned and cooked through, about 3 to 4 minutes. Transfer the chicken to a plate and set aside.
Warm the burrito-sized tortillas following the package instructions so they are pliable for rolling.
Assemble the burritos one at a time: place a portion of cooked chicken in the center of each tortilla, then top with diced avocado, shredded mozzarella, a spoonful of sour cream, a drizzle of Ranch dressing, and chopped cilantro.
Fold the bottom edge of the tortilla tightly over the filling, tuck the sides in, and roll up to enclose the filling completely. Repeat with remaining tortillas.
Reheat the cast-iron grill pan over medium-high heat. Place the burritos seam-side down in the pan and press gently with a spatula. Cook about 3 to 4 minutes per side, turning once, until each side is golden and the cheese inside has melted.
Serve the burritos immediately. To make ahead, assemble burritos, wrap and refrigerate; when ready to serve, bake in a preheated 375°F (190°C) oven until heated through and cheese is melted, about 15–20 minutes.