Combine tomato sauce, ketchup, brown sugar, Worcestershire sauce, mustard, garlic powder, onion powder, and black pepper in a bowl and whisk until smooth.
Heat olive oil in a large pan over medium heat.
Add diced onions and green bell peppers and cook until soft and slightly caramelized, about 5-6 minutes.
Stir in garlic and cook for 1 minute until fragrant.
Add ground beef and cook over medium heat until fully browned, breaking it apart as it cooks.
Drain excess grease if needed.
Pour the sauce over the browned beef and stir to combine.
Reduce heat to low and simmer for 15 minutes, stirring occasionally, until sauce thickens.
While beef simmers, whisk together half and half, cornstarch, onion powder, and garlic powder in a small saucepan.
Bring to a light boil over medium-high heat, whisking constantly.
Reduce heat to low and gradually stir in grated cheddar cheese until fully melted.
Add diced green chiles and season with salt to taste.
Keep warm on low heat, stirring occasionally.
Toast brioche buns in a hot skillet until golden brown on the cut sides.
Spoon beef mixture generously onto bottom halves of toasted buns.
Top with a generous ladle of warm queso and sliced jalapeños if desired.
Cap with top bun and serve immediately.