Hot Dog Buns

Ingredients (12)

• 1 package (1/4 ounce) active dry yeast
• 1 cup warm water (110° to 115°), divided
• 2 teaspoons plus 1/2 cup sugar, divided
• 1 cup warm milk (110° to 115°)
• 1/4 cup shortening
• 2 teaspoons salt
• 2 large eggs, room temperature
• 6 to 6-1/2 cups all-purpose flour
• TOPPING:
• 1 large egg, room temperature
• 1 tablespoon cold water
• Caraway, poppy or sesame seeds