Heat the oven to 400 degrees F. Scrub and dry the sweet potatoes and prick each one four or five times with a fork.

Rub the potatoes all over with the olive oil and kosher salt. Set them directly on the oven rack with a sheet pan on the shelf below to catch drips.

Bake 45 to 55 minutes, until a thin knife slides into the center with no resistance and syrup bubbles out of the fork holes.

Heat a 12 inch heavy skillet over medium-high heat for a full 2 minutes, empty, until a drop of water skitters across it.

Add the ground beef and press it into one flat layer covering the pan floor. Leave it completely undisturbed for 4 to 5 minutes so a brown crust forms.

Break the beef into chunks and cook 3 minutes more, then season with the salt and pepper.

Push the beef to one side, add the onion to the cleared space and cook 4 minutes until soft. Stir in the garlic, smoked paprika, chili powder and onion powder for 30 seconds.

Add the tomato paste and stir it constantly in the hot fat for 60 to 90 seconds, until it darkens from bright red to deep brick and smells sweet.

Pour in the beef broth and scrape the bottom of the pan hard for about 15 seconds to release the browned bits. Stir in the Worcestershire and Dijon.

Simmer 3 to 4 minutes until the beef is glossy and just barely saucy, holding its shape on a spoon rather than pooling. Taste and adjust the salt.

Switch the oven to broil. Split each baked potato lengthwise without cutting all the way through and open it like a book.

Fluff the flesh with a fork and push it toward the edges to make a trough. Divide the filling evenly among the four potatoes.

Scatter the grated sharp cheddar over the top and broil 2 to 3 minutes, watching constantly, until the cheese is melted with a few browned spots.

Scatter the sliced green onions over the top and serve right away.