Combine 1/4 cup warm water (about 110 degrees) with the milk in the bowl of a stand mixer fitted with a paddle attachment. Sprinkle the yeast over the mixture and let stand for about 8 minutes, stirring occasionally, until mixture looks foamy.
Add the flour and salt to the yeast mixture. With the mixer on medium-low, blend until shaggy lumps form, about 1-2 minutes. Add the eggs, one at a time, mixing well after each addition. Beat in sugar. Increase speed to medium and continue to mix for 3 minutes, until the dough is smooth.
Reduce the speed to low and add the butter one tablespoon at a time, making sure to beat well after each addition, about 4 minutes total. Increase speed to medium-high and beat until dough begins to pull away from sides of the bowl, about 8 minutes.
Spray a large bowl with nonstick cooking spray and place dough in bowl. Cover with plastic wrap and place in warm area until doubled in size, about 1 1/2 hours.
Punch down dough and lift around edges and let dough fall back into the bowl. Cover the bowl tightly with plastic wrap and chill in refrigerator deflating dough in similar fashion every 30 minutes until dough stops rising, about 1 1/2-2 hours. Chill dough overnight.
Spray 12 standard muffin cups with nonstick cooking spray. Divide the dough into 12 equal pieces. Cut each piece into 3 pieces. Roll each piece into a ball between the palms of your hands. Place 3 balls into each prepared cup. (see photo)
Place the muffin pan covered with a sheet of wax paper in a warm area to rise until almost doubled, about 50-60 minutes.
Place rack in center of oven and heat to 400 degrees. Place the muffin pan on a rimmed baking sheet. Brush egg wash over risen dough making sure that the wash doesn't drip between the dough and the pan.
Bake until golden brown, about 20 minutes, covering with foil if they appear to be browning too quickly. Transfer to a rack to cool for 10 minutes. Remove from pan. Serve warm or at room temperature.