To make cheeseburgers: In a bowl, mix ground beef, salt and pepper. Shape 1/4-ounce at a time into 1 1/2-inch patties. Broil or grill 30 seconds per side.
To assemble: At serving time, preheat oven to 350 degrees F. Slice buns in half. Layer ketchup, tomato and lettuce on each bottom half. Place burgers on baking sheet; top each with a slice of cheese. Bake until cheese melts, 2 to 3 minutes. Place in buns and serve.
To make the basic bread dough: In a small bowl, mix yeast, 1/2 teaspoon of sugar and 1/2 cup warm water. Let sit until foamy, about 5 minutes. In bowl of electric mixer fitted with a paddle, beat remaining 1 1/4 cups warm water, egg, powdered milk, 2 tablespoons sugar, salt and 1 cup flour. Beat until smooth and creamy, about 7 minutes. Add yeast mixture; beat on medium. On medium-low, beat in 3 1/2 cups flour, 1/2 cup at a time, until dough comes together (it will be sticky), about 2 minutes. Switch to dough hook. Gradually add butter; beat until dough is soft and sticks to fingers slightly, about 7 minutes. If dough is too wet, add 1/4 cup flour. On lightly floured surface, knead dough several turns into a ball. Cover dough with plastic. Let stand in warm place until it doubles in size, about 1 hour.
Preheat convection oven to 350 degrees F.
Coat parchment lined baking sheet with cooking spray. Roll dough into 3/4 inch balls; place 1 1/2 inches apart on baking sheet. Cover with plastic wrap lightly coated with cooking spray. Let stand on a warm place until doubled in bulk, about 20 minutes. Brush egg wash over dough; sprinkle with poppy seeds. Bake until golden brown, 8 to 10 minutes, rotating pan half way through. Cool buns on rack.
This recipe was provided by a chef, restaurant or culinary professional. It has not been tested for home use.