In the bowl of a stand mixer, add flour, sugar, salt, and undissolved yeast. Add in 2 eggs and set aside.
In a medium-sized saucepan combine milk, water, and butter; heat over medium heat until very warm (120° to 130°F). Add to the flour and egg mixture, beat 2 minutes on medium speed of, scraping the side of the bowl as neccesary.
Add 2 cups flour and beat at high speed 2 minutes, scraping bowl occasionally.
Change to a dough hook and add flour ½ cup at a time on low speed to make a soft dough; about 2 ½ cups additional (7 ½ cups total). Continue to knead on low for 6 minutes. If needed, add up to ½ cup of additional flour (⅛ cup at a time) until dough is no longer sticky, you want it to be elastic and smooth.
Cover the bowl with plastic wrap and let it rest for 10 minutes.
Divide dough into 3 equal pieces. Working with one-third at a time (cover the unused dough), divide each third into 36 pieces. Shape each piece into a 1-inch ball. Place 3 balls in each greased muffin pan cups.
Turn OFF the oven, very important!
Lightly cover rolls with foil; let rise in warmed oven until doubled in size, about 30-40 minutes.
Beat remaining egg slightly; brush on rolls. Sprinkle with poppy seeds.
Bake at 375°F for 12 to 15 minutes or until golden brown. If using dark nonstick muffin pans, rolls will cook quickly. Check for doneness at minimum bake time.
Immediately remove from pans. Serve warm. Or allow rolls to cool completely.
Store in an air-tight container and freeze for up to 1 month.