Preheat the oven to 400F.

Place the potatoes on a baking sheet and pierce each with a fork in a few places. Drizzle with olive oil and season with salt and pepper. Bake for 1 hour, up to 1 hour 15 mins, until the potatoes are tender when squeezed, then remove from the oven to let cool. Turn the heat down to 350F.

In a medium pot preheated over medium heat, melt the butter then add the garlic and flour. Cook while whisking for 1 min, then add the milk ½ cup at a time, whisking to fully incorporate it before adding more. Once all of the milk is added, turn the heat up to medium high and continue whisking until the white sauce starts to bubble and has thickened slightly, then add the kosher salt, pepper, and broccoli. Cook while stirring for 1-2 mins until the broccoli is almost tender, then add the shredded chicken and cheddar cheese. Cook for 1 min until the chicken is warm and the cheese is melted, then turn off the heat and cover the pot to keep warm.

Slice off the tops of the potatoes. Using a spoon, core out the insides of the potatoes and place them in a bowl. Mash with a potato masher until smooth. Set aside 1 cup of the creamy sauce and add the rest to the bowl with the potatoes. Mix and season to taste with salt and pepper.

Fill the potato shells with the potato mixture and place onto a baking sheet. Top each with the remaining creamy sauce and a sprinkle of shedded cheddar cheese. Place the potato tops flesh side up on the baking sheet and sprinkle each with cheese.

Bake at 350F for 15-18 mins until the cheese is melted and potatoes are warmed through. Broil for 1-2 mins at the end until the cheese gets golden brown spots. Top with fresh chives and enjoy!