The Perfect Burger and Bun

Name: The Perfect Burger and Bun
Ingredients: 1 lb. (450 grams) ground chuck or ground lean beef (i liked 10% fat the best); 2 tbs. finely chopped yellow onion; 1 tsp. minced garlic; 1 tsp. salt; ½ tsp. freshly ground pepper; 1 or 2 dashes of worcestershire sauce; 3 tablespoons (45 ml) warm milk; 2 teaspoons active dry yeast; 2½ (35 ml) tablespoons sugar; 2 large eggs; 3 cups (710 ml) bread flour**; ⅓ cup (80 ml) all-purpose flour**; 1½ teaspoons salt; 2½ tablespoons unsalted butter, softened; Sesame seeds (optional); If using all purpose and whole wheat flours, use 1.5 cups (355 ml) all purpose flour and 1.5 cups (355 ml) bread flour + 4 t (60 ml) vital wheat gluten