Preparation:

Step 1: Preheat the oven to 400°F (200°C). Pierce each potato several times with a fork to allow steam to escape. Place the potatoes on a baking sheet and bake for 45-60 minutes, or until they are tender and the skin is slightly crisp.

Step 2: While the potatoes are baking, prepare the filling. In a large mixing bowl, combine the shredded chicken, steamed broccoli, sour cream, butter, milk, salt, and pepper. Mix until all ingredients are evenly distributed, and the filling is creamy.

Step 3: Once the potatoes are baked and soft to the touch, carefully remove them from the oven. Let them cool slightly before handling. Using a knife, cut a slit along the top of each potato, and gently squeeze the sides to open them up. Scoop out some of the potato flesh to create space for the filling.

Step 4: Stuff each potato generously with the chicken and broccoli mixture. Ensure that the filling is evenly distributed among all four potatoes.

Step 5: Sprinkle the shredded cheddar cheese on top of the stuffed potatoes. Place them back in the oven for an additional 5-10 minutes, or until the cheese is melted and bubbly.

Step 6: Remove from the oven, garnish with freshly chopped chives, and serve hot.