Add the ground beef, hamburger seasoning, seasoned salt, and garlic powder to a large mixing bowl. Mix gently until just combined.
Divide the beef mixture into four equal portions, about 4 ounces each. Shape each portion into a thin patty approximately 5 inches in diameter. Make the patties slightly larger than the buns because they will shrink as they cook.
Press a shallow indentation into the center of each patty to help prevent the burgers from puffing up during cooking.
Preheat a large skillet over medium-high heat.
Cook the patties for about 4–5 minutes per side, or until they reach your preferred level of doneness. For food safety, ground beef should reach an internal temperature of 160°F.
Just before removing the patties from the skillet, place one slice of sharp cheddar cheese on each burger. Cover briefly to help the cheese melt.
While the patties cook, lightly toast the hamburger buns in a separate skillet or in the oven.
Spread cowboy butter over the cut sides of the toasted buns.
Place a cheesy beef patty on each bottom bun. Top with tomato, onion rings, crumbled turkey ham, and sliced jalapeños.
Drizzle barbecue sauce over the toppings, then add the top bun.
Serve immediately while the cheese is melted and the onion rings are crisp.