Heat the oven to 425F. Scrub and dry the sweet potatoes, prick each one four or five times with a fork, and rub with a little olive oil and half the kosher salt.

Set the potatoes directly on a rimmed baking sheet, no foil, and bake 45 to 55 minutes until a knife slides into the thickest part with no resistance.

With about 20 minutes left, toss the broccoli florets with the olive oil, garlic powder, smoked paprika, and remaining salt. Spread them around the potatoes in a single layer with space between the florets.

Roast until the floret edges are browned and slightly crisp, then squeeze the lemon over the hot broccoli.

Melt the butter in a small saucepan over medium heat, whisk in the flour, and cook for a full minute until it smells faintly nutty.

Pour in the milk slowly while whisking, bring to a gentle simmer, and cook 2 to 3 minutes until it coats the back of a spoon.

Take the pan completely off the heat. Add the grated cheddar in three handfuls, stirring each one until it melts fully before adding the next.

Stir in the mustard powder, black pepper, and a pinch of salt. Loosen with a splash of warm milk if the sauce stiffens.

Split each hot potato lengthwise about three quarters of the way through, then press the ends toward each other so the flesh opens up.

Fluff the flesh with a fork and season with a small pinch of salt.

Fill each potato with roasted broccoli, pour the cheddar sauce over the top, and finish with sliced chives. Serve right away.