Preheat the oven to 400 degrees Fahrenheit. Scrub the sweet potatoes well, then pierce each potato a few times with a fork. Bake directly on the oven rack for 45 to 50 minutes, or until the skins are crispy and the centers feel soft when pierced with a knife.
While the potatoes bake, heat a skillet over medium heat. Add the ground beef and cook until it starts to brown, breaking it up with the spatula as it cooks.
Add the chopped onion and minced garlic to the skillet. Cook until the onion is translucent and the beef is fully browned, about 4 to 5 minutes.
Stir in the tomato sauce, ketchup, mustard, salt, and pepper. Let the mixture simmer for 5 minutes, until it thickens slightly and flavors meld.
When the potatoes are done, let them cool for a few minutes. Slice each potato in half lengthwise and gently fluff the inside with a fork. If you like a crisper texture, you can broil the halves for 2 minutes before stuffing.
Spoon the sloppy joe filling into each potato half. If using cheese, sprinkle it over the top and bake for another 3 to 5 minutes until melted and bubbly.
Finish with a sprinkle of green onions or extra pepper if you want a bright finish. Serve warm.