Heat milk, sugar, butter, and a pinch of salt gently in a saucepan until warm and butter is almost melted. Do not boil.
In a mixing bowl, combine 1½ cups flour with yeast. Add the warmed milk mixture and eggs. Beat on medium speed for about 3 minutes until combined. Gradually mix in remaining flour until dough is smooth and elastic.
Shape dough into a ball, place in a lightly greased bowl, and cover. Allow to rise until doubled in size (1-2 hours).
Punch dough down and rest for 10 minutes. Roll into a 20x16-inch rectangle. Spread with melted butter mixed with brown sugar, cinnamon, and vanilla. Cut dough into twenty 1-inch strips crosswise.
Fold each strip in half, then twist several times. Arrange twists about 2 inches apart on parchment-lined baking sheets. Let rise until doubled (about 45 minutes).
Preheat oven to 375°F (190°C). Brush with egg wash. Bake twists for 12-15 minutes until golden brown.
Whisk powdered sugar, vanilla, and milk until drizzling consistency. Drizzle over warm twists.