In a large bowl, toss the potatoes with the olive oil and salt to coat. Place the potatoes directly on the baking rack and bake for 50-60 minutes or until done.
While the potatoes are cooking, melt the butter in a medium sauce pan and whisk in the cornstarch. Cook the mixture until it starts to turn golden and then slowly whisk in the milk. Stir in the garlic powder, nutmeg, salt and pepper. Cook the mixture until it begins to thicken, approximately 3-4 minutes. Add both cheeses and stir until smooth.
Transfer the potatoes to a serving platter and slice down the middle being careful to not cut all the way through. Pinch the sides of the potato at each end of the slit and press to open. Season the inside of the potato with salt and pepper if desired. Stuff the potato with the chicken and broccoli and top with cheese sauce. Serve immediately.