Whisk together flour, salt, sugar, and yeast in your large bowl. In a microwave-safe measuring cup, add water and milk. Microwave for 45 seconds, until very warm. Whisk 1 egg in separate bowl.
Set your mixer on low, then add in light butter. Mix for about a minute, or until butter is distributed through flour mixture.
Turn the speed up to medium and slowly add in your wet ingredients, including the whisked egg. "Knead" the dough with your mixer for about 5 minutes, or until dough is slightly elastic. (See blog notes for using a food processor instead.)
Use a spatula to form the dough into a ball. Cover and let rise in a warm place until more than doubled in size, about 45 minutes-1 hour.
Dust a cutting board with 1 tbsp flour. Use the extra tbsp to flour your hands. Scrape the dough onto your cutting board and knead just until the dough is not as sticky.
Grease a 13x9 baking pan. Cut dough into 24 portions, roll each into a small disk, and place in your baking pan. You should have 6 rows of dough balls, 4 of each across (see picture above).
Cover and let rise again. The rolls should rise until they are fully touching each other.
Preheat oven to 350F Whisk remaining egg with 1 tbsp water. Lightly brush tops of rolls with egg wash. Bake for 20-25 minutes, broiling in the last 30 seconds if the tops aren't brown enough.