Preheat the oven to 400°F (200°C) and line a baking sheet with foil.
Season the chicken chunks with chili powder, ground cumin, onion powder, garlic powder, and freshly ground black pepper (add salt if desired).
Heat 1 Tablespoon olive oil in a large skillet over medium heat and cook the chicken, turning once, until golden and cooked through, about 6–10 minutes depending on size.
Transfer the cooked chicken to a plate, let rest a few minutes, then shred into small pieces.
In a large bowl, combine the shredded chicken with 1/3 cup ranch dressing, 1/2 cup of the shredded Mexican blend cheese, and the chopped cilantro; mix to combine.
Spoon a generous portion of the chicken filling down the center of each tortilla, fold the bottom edge over, fold in the sides, and roll tightly into burritos.
Place the burritos seam-side down on the prepared baking sheet and brush the tops with olive oil or spray with nonstick spray.
Bake at 400°F (200°C) for 20–25 minutes, until the tortillas are golden brown and crispy.
While the burritos bake, make the sauce: melt 2 Tablespoons butter and 2 Tablespoons olive oil in a medium saucepan over medium heat.
Whisk in 1/4 cup flour and cook, stirring, for about 2 minutes to form a roux.
Add 1/2 teaspoon cumin, then gradually whisk in the 2 cups chicken broth and cook, stirring, until slightly thickened, about 3 minutes.
Remove the saucepan from heat and whisk in the dry ranch seasoning packet and 1/2 cup sour cream until smooth; keep warm.
Remove the baked burritos from the oven and set the oven to high broil.
Ladle a spoonful of the ranch sauce over each burrito and sprinkle the remaining shredded cheese on top.
Broil the sauced burritos 2–3 minutes, until the cheese is melted and bubbly; watch closely to avoid burning.
Remove from oven and top with diced avocados and tomatoes if desired, then serve.