Melt Butter: Melt 3 tablespoons of unsalted butter in a thick-bottomed pot over heat.
Mix Wet Ingredients: Turn off the heat and add 1/2 cup whole milk, 2 tablespoons sugar, 1/4 teaspoon salt, and 1 large egg to the pot. Mix until well combined.
Activate Yeast: Add 2 teaspoons of active dry yeast to the mixture and let it sit for 1 minute to activate.
Add Flour: Mix in 1 1/2 cups of all-purpose flour until well combined and sticky.
First Rise: Cover the pot and let the dough rise for 1 hour or until doubled in size.
Knead and Second Rise: Deflate the dough and knead for about 1 minute. Let it sit for 30 more minutes.
Shape Rolls: Divide the dough into 6 equal parts, roll into thin ropes, coil, and tuck the ends to form rolls.
Final Rise: Let the shaped rolls rise for 1 hour or until they expand and are ready to bake.
Preheat Oven and Brush Rolls: Preheat the oven to 350°F (177°C). Brush the rolls with egg white for a shiny finish.
Bake: Bake the rolls in the preheated oven until golden brown and cooked through.