In a bowl, whisk together ketchup, beef broth, Worcestershire, yellow mustard, brown sugar, and apple cider vinegar; set near the stove.
Set a large skillet over medium heat. Add the ground beef, salt, and pepper, and cook 3–4 minutes, breaking it into small crumbles as it releases some fat.
Scoot the beef to one side. In the open space, add the onion and bell pepper and cook in the rendered fat until softened, about 3 minutes. Stir in the garlic for 30 seconds.
Sprinkle in the chili powder and smoked paprika, then add the tomato paste. Stir to coat everything and cook 1–2 minutes to bloom the spices and lightly caramelize the paste.
Pour in the ketchup mixture, scraping up any browned bits from the pan. Bring to a gentle simmer, then reduce heat to medium-low, cover, and cook for 5 minutes.
Uncover and continue to simmer, stirring occasionally, 4–6 minutes until the sauce is thick, glossy, and clings to the beef. If it tightens too much, splash in a bit more broth; if too loose, simmer an extra 2–3 minutes.
Turn off the heat, taste, and adjust salt or pepper. Let the mixture rest 2–3 minutes so it sets up before spooning onto toasted buns.
Tip: For extra-fine crumbles, press a potato masher over the beef midway through browning.