1-Following a step-by-step guide helps you create the perfect homemade brioche hot dog buns with ease. Start by preparing all ingredients; in a large bowl, whisk together 3 1/3 cups all-purpose flour or bread flour (453g), 1 1/2 teaspoons instant yeast, 2 tablespoons sugar, and 1 1/2 teaspoons kosher salt. This sets the base for a great rise and texture in your brioche sandwich rolls for hot dogs.

2-Next, in a small saucepan, heat 3 tablespoons whole milk and 3 tablespoons of the butter until the butter melts; let it cool slightly. In a medium bowl, whisk 1 cup lukewarm water and one large egg, then add the milk and butter mixture before pouring it into the dry ingredients. Stir with a wooden spoon until it forms a sticky dough, cover, and let it rise for 2 to 4 hours at room temperature until doubled in size, or refrigerate for 12 to 24 hours for a slow rise.

3-Once risen, turn the dough onto a floured surface, shape it into a rectangle, and divide it into 10 equal portions. Shape each piece into a ball, roll it into a 6-inch rectangle, fold it into thirds like a letter, tuck the ends under, and place seam-side down on a parchment-lined baking sheet in 2 rows of 5 with 1/2-inch space between them. Cover and let rise until puffy, about 1 to 2 hours.

4-Preheat and Bake: Preheat the oven to 375°F and whisk the remaining large egg with 1 tablespoon water to brush over the buns. Bake for 12-15 minutes, rotating the baking sheet halfway, until golden brown. Immediately after baking, melt the remaining 2 tablespoons butter and brush it over the tops of the hot buns, then allow them to cool on a wire rack.