Heat a medium saucepan over medium heat and add 2 tablespoons olive oil. When the oil is hot, add half of the diced white onion and cook until translucent, about 5 minutes.
Add the ground beef, 1/2 teaspoon kosher salt, and the minced garlic, breaking up the meat and cooking until browned, about 5 minutes. If using leaner ground beef, add a teaspoon or two of olive oil to prevent sticking.
Stir in the 1/3 cup tomato paste, 2 cups beef broth, 1/2 teaspoon ground cumin, and 1/4 teaspoon ground cayenne. Cook, stirring, for about 1 minute, then reduce the heat to low and cover the pot to keep the chili warm while you finish the rest of the meal.
Cook the hot dogs on a preheated grill or in a hot grill pan over high heat, turning until grill marks appear and the hot dogs are cooked through. Transfer the cooked hot dogs to a 200 degree F oven to keep warm.
Toast the hot dog buns in a grill pan: add a teaspoon of butter to the pan and, when very hot, press the buns down in the pan for about 1 minute, then toast the opposite side for an additional 30 seconds. Repeat with remaining buns.
Assemble the dogs by placing each hot dog in a toasted bun, adding yellow mustard, topping with a generous spoonful of the chili and then 1/2 cup cheddar cheese (or other melty cheese). If the cheese isn't melting, place the assembled hot dogs under the broiler for about 1 minute. Finish with the remaining diced white onion and pickled jalapeños as garnish.