Wash hands with soap and water for 20 seconds.
Do not taste or eat any raw dough or batter made with uncooked flour and/or raw eggs.
Heat milk, water, and butter until 115-120°F. Butter does not need to melt.
In mixing bowl, combine 3 cups of flour, salt, yeast, and sugar.
Add milk mixture. Beat well. Beat in two eggs.
Continuing beating, adding flour as needed, until soft dough forms.
Sprinkle flour on a clean surface. Remove dough from bowl and knead until smooth and satiny.
Place in a covered bowl and let rise until doubled, approximately 1 1/2 to 2 hours.
Make the filling by combining brown sugar, cinnamon, and butter to form a paste.
Flour surface and roll dough out to a very large rectangle. Keep edges as straight as possible.
Spread filling paste over entire rectangle leaving about 1/2-inch of one long edge plain.
Roll up towards plain long edge, pinch to seal.
Cut into 12 even pieces. Place in two 9x13 baking dishes that are lined with parchment paper.
Cover and let rise until about doubled, approximately 1 hour.
Bake at 325°F (glass pan) or 350°F (metal pan) until brown and done in the middle of the rolls. The internal temperature in the center of the rolls should be 188°F. Bakes for 30-45 minutes.
While rolls are baking, make the icing. Beat together powdered sugar, salt, vanilla, butter, and 2 Tablespoons milk. Add additional milk as necessary until icing is spreadable.
Just after removing rolls from oven, frost with about 1/3 to 1/2 of icing. It will melt down into the rolls. After rolls have cooled, frost with the remainder of the icing.