In a medium bowl, combine 0.5 lb ground beef, 2 tbsp breadcrumbs, 1 tbsp milk, 1 tsp salt, and 1/4 tsp black pepper. Gently mix with your hands or a fork until just combined — do not overwork the meat to keep patties tender.

Form patties

Divide the mixture into two even portions. Shape each portion into a flat round patty about 3–3.5 inches (7–9 cm) across and roughly 1/2 inch (1.2 cm) thick. Press a slight shallow indentation in the center of each patty with your thumb to prevent puffing while cooking.

Cook

Heat a nonstick skillet or small cast-iron pan over medium heat. Add 1 tsp unsalted butter and allow it to melt and coat the pan. Place the patties in the skillet and cook for 3–4 minutes on the first side until a brown crust forms. Flip and cook another 2–3 minutes on the second side for medium doneness (longer if you prefer well done).

Melt cheese

About 1 minute before the patties are done, place 1 slice of cheese on each patty and cover the pan briefly (30–60 seconds) or add a splash of water (1–2 tsp) and cover to steam the cheese until melted.

Buns & Assembly

Toast buns

While patties cook, spread 1 tsp butter across the cut sides of the 2 buns. Toast them butter-side down in a separate skillet over medium heat or on a griddle until golden, about 1–2 minutes.

Prepare toppings

Lay out 2 leaves of lettuce (tear to kid-friendly size), prepare 4 pickle slices if using, and combine 2 tbsp ketchup and 1 tbsp mayonnaise if you want a simple sauce (or place separately).

Assemble burgers

Place a toasted bun bottom on a plate, add a small smear of ketchup or the ketchup-mayo sauce, then the cheesy patty, 2 pickle slices, and a small piece of lettuce. Top with the bun top. Serve immediately while hot.

Side (Optional)

Serve 1 cup of baby carrots or a portion of oven fries alongside the burger with 2 tbsp ranch or kid-friendly dip. If using oven fries, reheat or bake according to package directions until warm and crisp (typically 12–18 minutes at 425°F/220°C).