Make the BBQ Chicken: Preheat the oven to 375°F. Line a rimmed baking sheet with parchment paper or lightly spray with nonstick cooking spray.
Place 2 chicken breasts (5–6 ounces each, pounded to about ¾-inch thick) in a bowl. Add 1 tablespoon olive oil, 1 tablespoon paprika, 1 teaspoon cumin powder, 1 teaspoon garlic powder, 1 teaspoon onion powder, 1 teaspoon oregano, 1 teaspoon chili powder, ½ teaspoon salt, and ½ teaspoon black pepper. Toss with tongs until the chicken is evenly coated.
Arrange the seasoned chicken on the prepared baking sheet. Brush the tops with ¼ cup BBQ sauce, reserving the remaining ¼ cup BBQ sauce.
Bake for 10 minutes, then flip the chicken and brush with the remaining ¼ cup BBQ sauce.
Continue baking for 8–10 minutes, or until the chicken reaches an internal temperature of 165°F.
Remove the chicken from the oven and let it rest for a few minutes, then chop or cube it. Set aside.
Assemble the Nachos: Increase the oven temperature to 400°F (optional but recommended for crispier chips).
Line a large baking sheet with parchment paper. Arrange tortilla chips in an even layer, slightly overlapping but not piled.
Sprinkle 1½ cups shredded cheddar cheese and 1½ cups shredded Monterey Jack cheese evenly over the chips.
Bake for 8–12 minutes, or until the cheese is fully melted and bubbly.
Remove from the oven and immediately sprinkle the chopped BBQ chicken evenly over the nachos.
Finish with toppings to taste, including diced tomatoes, diced red onion, sour cream, chopped cilantro, sliced olives, and guacamole. Serve immediately.