1. Preheat your oven to 400 F (200 C). Scrub the potatoes clean under cold water, then pat them completely dry. Prick each potato several times with a fork. You can rub them lightly with olive oil and sprinkle with salt if desired for crispier skin. Place the potatoes directly on the oven rack and bake for 45-60 minutes, or until they are fork-tender.

2. While the potatoes are baking, steam or boil your broccoli florets until they are tender-crisp, about 3-5 minutes. Drain well and set aside. You want them cooked but still with a bit of bite.

3. In a large saucepan or Dutch oven, melt the butter over medium heat. Once melted, whisk in the flour and cook for 1-2 minutes, stirring constantly, to create a roux. This helps thicken the sauce.

4. Gradually whisk in the milk, a little at a time, ensuring no lumps form. Continue to cook, stirring frequently, until the sauce thickens and comes to a gentle simmer. Remove from heat and stir in the salt, pepper, garlic powder, and 1 1/2 cups of the shredded cheddar cheese until smooth and melted.

5. Add the cooked shredded chicken and the steamed broccoli florets to the cheese sauce. Stir gently until everything is well combined and coated in the creamy sauce. Keep warm over very low heat or off the heat while you prepare the potatoes.

6. Once the potatoes are baked and cool enough to handle, carefully slice each potato lengthwise down the center, being careful not to cut all the way through. Fluff the inside of the potato with a fork. You can scoop out some of the potato flesh into the chicken and broccoli mixture for an even creamier filling, mashing it slightly.

7. Generously spoon the creamy chicken and broccoli mixture into each baked potato. Top with the remaining 1/2 cup of shredded cheddar cheese. You can return them to the oven for a few minutes to melt the cheese, or serve immediately with your favorite toppings.