Preheat the oven to 375°F.
In a saucepan, heat ¾ cup milk, sugar, ⅓ cup butter, and salt, stirring until warm and the butter is almost melted. Be careful not to let it get too hot or boil.
In a mixing bowl, combine 1 ½ cups of flour and yeast. Add the warm milk mixture to the flour mixture along with the eggs. Beat on medium speed for about 3 minutes or until the flour is fully incorporated. Gradually add the remaining flour and knead until the dough is smooth and elastic.
Shape the dough into a ball and place it in a lightly greased bowl, turning it to coat both sides with oil. Cover the bowl and let the dough rise in a warm place until it doubles in size, which will take 1-2 hours depending on the room temperature.
Once risen, punch the dough down, place it on a lightly floured surface, and let it rest for 10 minutes.
Roll the dough into a 20 x 16-inch rectangle.
In a saucepan, melt ⅓ cup butter, then add brown sugar and cinnamon. Mix well and let it cool slightly. Spread the mixture over the dough. Cut the dough crosswise into twenty 1-inch strips.
Fold each strip in half, end to end, and twist several times. Arrange the twists on two parchment-lined baking sheets, spacing them about 2 inches apart. Allow the twists to rise until doubled in size, about 45 minutes.
Bake the twists in the preheated 375°F oven for 12-15 minutes, or until golden brown.
In a small bowl, mix together powdered sugar, vanilla, and enough milk to achieve a drizzling consistency. Drizzle the glaze over the twists and enjoy!