In a small saucepan, heat the milk over medium heat until warm (not boiling). Remove from heat and stir in the sugar and melted butter. Let cool slightly.
In a mixing bowl, combine the warm milk mixture with the active dry yeast. Let it sit for about 5-10 minutes until frothy.
In a large mixing bowl or stand mixer, add 2 cups of flour, eggs, salt, and yeast mixture. Mix well, gradually adding in the remaining flour until a soft dough forms.
Knead the dough on a floured surface for about 5-7 minutes until smooth and elastic. Alternatively, use a stand mixer with a dough hook for 5-6 minutes.
Place the dough in a greased bowl, cover with plastic wrap or a towel, and let it rise in a warm place until doubled, about 1 hour.
Once risen, punch down the dough and roll it out on a floured surface into a 16x12 inch rectangle.
Spread the softened butter over the dough, then sprinkle with brown sugar and cinnamon evenly over the surface.
Roll the dough tightly starting from the long edge, forming a log. Pinch the seam to seal. Cut into 12 even pieces.
Place the rolls in a greased baking dish. Cover and let them rise again for 30 minutes, until puffy.
Preheat the oven to 350°F (175°C) and bake the rolls for 25-30 minutes, until golden brown.
While the rolls bake, whisk together powdered sugar, milk, and vanilla extract in a small bowl until smooth.
Drizzle the glaze over warm cinnamon rolls as soon as they're out of the oven.