Place 3 tablespoons ketchup, 2 tablespoons mayonnaise, 1 tablespoon yellow mustard, 1 teaspoon Worcestershire sauce, 1 teaspoon smoked paprika, 1 teaspoon chili powder, 1 teaspoon toasted sesame oil, and 1/2 teaspoon kosher salt in a large bowl and whisk until combined.
Finely chop 1 small shallot (about 1/4 cup), thinly slice 1 medium scallion (about 2 tablespoons), and stack and chop 8 slices American cheese into 1/2-inch pieces. Add these to the bowl, separating the cheese pieces as you go.
Add 12 ounces ground beef to the bowl and mix with your hands until everything is well-combined and the cheese is evenly distributed.
Fill a small bowl with water and line a baking sheet with parchment paper. Place 6 round dumpling wrappers on a work surface. Scoop about 1 1/2 teaspoons of the filling in the center of each wrapper, making sure there is cheese in each portion, and flatten it out a little bit.
Dip your finger into the water and gently trace around the edges of a wrapper to dampen. Fold in half by bringing the bottom up to the top and pinching together just at the top. Create pleats on the side of the wrapper facing you by starting to the left of the center pinch: Use your index finger and thumb to gather and fold a pleat toward the right and pinch to seal. Repeat with two more pleats to the left until you reach the end. Repeat folding three pleats to the right of the center pinch. Pinch tightly and make sure the filling is completely sealed in the wrapper. (Alternatively, you can skip the pleating altogether by just folding the wrapper in half over the filling and pinching to seal.)
Pick up the dumpling by the pleats and place down on the baking sheet to form a flat bottom. Repeat until all the dumplings are formed, making sure they don’t touch on the baking sheet.
Cook the dumplings in batches: Heat 1 tablespoon of the vegetable oil in a large nonstick frying pan over medium-high heat until shimmering. Add 10 to 12 dumplings flat-side down, making sure they do not touch. Cook until the bottoms are light golden-brown, 1 to 2 minutes. Add 1/4 cup water, cover, and cook until the wrappers have completely softened and the water has evaporated, 3 to 4 minutes. Uncover and cook until the bottoms are dark golden-brown, 1 to 2 minutes.
Transfer to a plate and repeat with the remaining oil, dumplings, and water. Garnish with roasted sesame seeds if desired and serve immediately.