Preheat oven to 400 degrees F.
Begin by baking the potatoes, as this will take the longest. Place potatoes onto a baking sheet. Pierce with a fork, drizzle with olive oil and season with salt. Place into preheated oven and bake for about 1 hour.
While they are baking prepare the stuffing. Make a mornay sauce by combining the butter and flour over medium heat and then whisking in the milk. Fold in about 2 cups cheese and stir until melted. Once melted, remove from heat and fold in the cooked broccoli florets, crispy bacon bits, chopped chives and season with salt and freshly ground black pepper.
When the potatoes are done make a cut across the top and squeeze it from the bottom so a small pouch opens up and the bottom is squared off. Spoon the filling over the top of the potato, sprinkle with cheese, season with pepper, to taste, and then pop in the oven for 2 more minutes until golden brown and bubbly.