Microwave prep: In a large bowl, warm the milk in the microwave for 10 second increments until it reaches 100 degrees Fahrenheit. Set aside. In a small bowl or microwaveable cup, melt the butter in 5 second increments and set in the fridge to cool slightly.
Mix: In the bowl with the warm milk, add the sugar and yeast and mix gently. Set aside for 5-10 minutes. (Setting aside is optional for instant yeast, but it does help the ingredients distribute).
Add: To the yeast mixture, add the sourdough starter, melted butter, eggs and mix until combined.
Mix flour and salt: In a separate bowl mix 3 ½ cups of flour and salt together. Combining the salt with the flour keeps it from reacting negatively to the sourdough starter.
Add: Add the flour mixture to the wet ingredients and mix until a soft wet dough forms. Add the remaining flour until the dough is tacky but not overly sticky.
Knead: Knead by hand for 10 minutes, adding flour as necessary, until the dough is smooth, elastic and slightly tacky but not sticky to the touch. You cannot over-knead dough by hand. Make sure to knead thoroughly. This is key for fluffy rolls.
Warm Bulk Rise: Cover with plastic wrap or a warm tea towel and let rise in a warm spot until doubled in size, usually 45-60 minutes.
Shape: Using a rolling pin on a floured surface, roll the dough in a rectangle until the dough is ½ inch thick. Using a pizza slicer, cut the dough into rectangles (for that classic Texas Roadhouse shape) and place on a baking sheet pan lined with parchment paper. Let rise for 30-45 minutes, until puffy.
Bake: Bake at 350 degrees Fahrenheit for 18-22 minutes until the tops are golden. While the rolls are in the oven, melt the remaining 2 tablespoons of butter.
Brush: Remove the rolls from the oven and immediately brush the tops of the rolls with melted butter.