Chef John's White Bread
1 (.25 ounce) package active dry yeast 1 large egg, beaten 1 pinch cayenne pepper 1 tablespoon all-purpose flour, or as needed 1 tablespoon white sugar 1 tablespoon white vinegar 1 teaspoon fine salt 1 ¼ cups whole milk, warmed 2 tablespoons melted butter, divided 2 ¾ cups all-purpose flour, or more as needed 3 tablespoons unsalted butter, very soft ¼ teaspoon baking soda