In a large bowl, combine ground beef, eggs, crushed potato chips, crumbled bacon, dry mustard, garlic powder, salt, and pepper. Mix gently with your hands until fully combined; do not overmix.
Shape the mixture into 4 equal patties (about ½-inch thick). Set aside.
In a large 12-inch skillet, heat the butter and olive oil over medium heat. Add the patties and cook for 4 to 5 minutes per side, or until browned and cooked through to an internal temperature of 160°F.
Remove patties to a plate and carefully drain excess grease, leaving about 1 tablespoon in the skillet.
Add the sliced onion and diced jalapeño (if using) to the skillet. Cook, stirring occasionally, until onions are golden and softened, about 6 to 8 minutes.
In a small bowl, whisk together beef broth and cornstarch until smooth.
Pour in the beef broth mixture, then stir in the BBQ sauce and Worcestershire sauce. Bring to a gentle simmer and cook for 2 to 3 minutes, until the gravy starts to thicken. If needed, adjust the consistency with a little extra broth, or add more BBQ sauce for a stronger flavor.
Return the cooked patties to the skillet, nestling them into the gravy. Spoon gravy over the tops. Simmer gently for 2 to 3 minutes to heat through and let the flavors develop.
Serve hot, spooning extra cowboy gravy over each patty.