Preheat oven to 425°F. Lightly coat the potatoes with olive oil, sprinkle with salt and pepper.
Prick potatoes with the tines of a fork about four times. Place on a baking sheet lined with foil. Bake potatoes for 50 to 60 minutes, flipping over after 40 minutes of baking until skin is crispy and a knife inserted into the center has no resistance. In the meanwhile make the topping ingredients.
Chicken
Season both sides of the chicken breasts with salt, pepper, and paprika. Heat a large frying pan or cast iron skillet over medium-high heat. Add one tablespoon of oil and allow it to heat up.
Carefully add the chicken breast and allow it to cook for 6 minutes. Flip to the other side, reduce heat to medium and cook another 6 to 7 minutes, or until no longer pink and the internal temperature of the chicken reaches 165°F.
Transfer to a clean plate to allow to rest and cool slightly. Once slightly cooled, chop the chicken into ½ inch cubes.
Cheese Sauce
Melt the butter in a medium-sized saucepan over medium heat until foamy. Add flour and whisk to combine until beige paste forms, stir and cook for about 1 to 2 minutes. Add milk and whisk to combine.
Increase heat to high and bring mixture to a boil, whisking continuously. Reduce heat to a medium simmer, cook for 5 to 8 minutes, or until sauce is thickened.
Add in ¼ teaspoon chipotle pepper (optional if you want it a little spicy), ¼ teaspoon salt, and ⅛ teaspoon pepper, whisk to combine.
Turn off the heat and slowly add in the cheese, whisk to combine until the cheese is melted and the sauce is smooth. Taste and add more seasoning as needed. Set aside.
Broccoli
In a medium-sized saucepan fitted with a lid, add 1-inch of water to the bottom of the pot and place steamer inside. Bring water to a boil, place broccoli in the steamer and cover.
Cook until broccoli florets are bright green and tender, about 2 to 3 minutes. Transfer to a bowl and lightly season with salt and pepper.
Assembly
Cut the hot baked potatoes through the center, creating an opening for the toppings. Use a fork to fluff the inside. Fill with cheese sauce, diced chicken, and broccoli.