Step 1

Preheat oven to 400°F. Heat 1 teaspoon of the oil in a large oven-proof skillet over medium-high. Add ground beef and 1 teaspoon of the salt, and cook, stirring occasionally, until browned and cooked through, 6 to 8 minutes. Transfer beef to a plate lined with paper towels. Discard drippings. Add onion, bell pepper, 1/2 teaspoon of the salt, and remaining 1 teaspoon oil to skillet, and cook over medium-high, stirring occasionally, until softened, 4 to 5 minutes. Add garlic, and cook, stirring constantly, until fragrant, about 30 seconds. Add tomatoes, ketchup, mustard, relish, Worcestershire, chili powder, cooked beef, and remaining 1 teaspoon salt to skillet, and stir to combine. Bring to a simmer over medium-high, and simmer 3 minutes. Remove from heat.

Step 2

Top sloppy joe mixture with Cheddar cheese. Shingle rolls on top, and brush with melted butter. Bake in preheated oven until rolls are warmed through and cheese is melted, about 10 minutes.