2 tablespoons plus 2 teaspoons olive oil
1 medium onion, dices small (2 cups)
1 large celery stalk, diced small (1/2 cup)
1/2 green bell pepper, diced small (1/2 cup
course salt and ground pepper
2 teaspoons minced garlic
1 1/2 pounds lean ground beef
3 tablespoons dark-brown sugar
3 tablespoons Worcestershire sauce
2 cups prepared tomato sauce
1 cup homemade beef or chicken stock or low-sodium chicken broth
2 teaspoons hot-pepper sauce (optional)
4 hamburger buns, split (I used whole wheat buns)
In a large skillet, heat 2 teaspoons oil over medium-high. Add onion, celery, bell pepper, season with salt and pepper, and cook until vegetables soften, about 2 minutes. Add garlic and cook 1 minutes. Add beef, breaking up meat with a wooden spoon, and cook until browned, 2 minutes. Add brown sugar, Worcestershire sauce, tomato sauce, and stock and bring to a boil. Reduce to a simmer and cook, stirring occasionally, 15 minutes. Add hot-pepper sauce (if using) and remove beef mixture from heat.
Meanwhile, heat broiler, with rack in top position. Place buns, cut side up on a baking sheet and lightly brush with 2 tablespoons oil. Broil until buns are golden, about 3 minutes. (Alternatively, toast on a grill pan or in a skillet oiled side down, over medium-high.)
Generously spoon beef mixture over toasted bun bottoms. Sandwich with bun tops and serve.