Preheat the oven to 350 degrees F. Poke a few holes in the potatoes with a fork. Bake until tender, 50 to 60 minutes.
Meanwhile, bring a pot of water to a boil and fill a bowl with ice water. Blanch the broccoli by throwing the florets into the boiling water until bright green and still slightly crisp, 1 1/2 to 2 minutes. Immediately drain the broccoli and plunge it into the bowl of ice water to stop the cooking process. Remove it from the ice water and set it aside.
In a skillet over medium heat, add 1/4 inch of vegetable oil. Add the onions and fry until browned and crisp, 15 to 20 minutes. Drain on paper towels and keep warm.
In another skillet, melt the butter over medium heat. Whisk in the flour and cook for a minute or 2, but do not let the flour brown. Whisk in the milk and cook until it thickens. Turn the heat to low, stir in the Cheddar and pepper Jack and cook until they are melted. Add the broccoli and cook, stirring, until the broccoli is warmed through.
Make a slit down the length of each potato using a fork. Push in the ends to open up the potatoes and break up some of the potato inside. Pour a ladle of the cheese sauce over each potato. Garnish with the crispy onions and serve while hot.