Dice the sweet potatoes: Peel the sweet potatoes and cut them into even 1/2-inch cubes. Keeping the pieces the same size helps them cook at the same rate during the simmer step.

Brown the ground beef: Heat a large skillet over medium-high heat and add the ground beef, breaking it apart with a spoon. Cook for about 6 minutes, until no pink remains, then transfer to a plate and drain excess grease from the pan.

Sauté the onion and peppers: Add olive oil to the same skillet and heat over medium. Add the onion and bell peppers and cook for about 4 minutes, stirring occasionally, until they soften.

Add the garlic: Stir in the minced garlic and cook for 30 seconds, just until fragrant. Watch it closely so it doesn't burn.

Add sweet potatoes and broth: Add the diced sweet potatoes and beef broth to the skillet. Stir to combine, then cover and reduce heat to medium-low.

Simmer until tender: Let the sweet potatoes simmer, covered, for 12 to 15 minutes, stirring once or twice. They're ready when a fork slides through them easily.

Season the mixture: Stir in the chili powder, cumin, smoked paprika, garlic powder, salt, and black pepper. Mix well so the spices coat the sweet potatoes evenly.

Combine beef and tomatoes: Return the cooked ground beef to the skillet along with the diced tomatoes with green chilies. Stir everything together and simmer, uncovered, for 5 minutes.

Top with cheese: Sprinkle the shredded cheddar cheese evenly over the top of the skillet. Cover and let it sit over low heat for 2 to 3 minutes, until melted.

Garnish and serve: Remove the skillet from the heat and sprinkle with chopped cilantro. Serve hot with lime wedges on the side.