In a large mixing bowl, combine warm milk, yeast, and sugar. Let it sit for 5 minutes until frothy.
Add melted butter, eggs, and salt to the yeast mixture. Gradually add flour and mix until a dough forms.
Knead the dough on a floured surface for about 5-7 minutes until smooth and elastic. Place in a greased bowl, cover, and let rise for 1 hour or until doubled in size.
Roll out the dough into a rectangle. Spread softened butter over the dough. Sprinkle brown sugar and cinnamon evenly over the butter.
Roll up the dough tightly and cut into 12 rolls. Place in a greased baking dish. Cover and let rise for another 30 minutes.
Preheat oven to 350°F (175°C). Bake the rolls for 25 minutes or until golden brown.
While the rolls are baking, prepare the maple glaze by mixing melted butter, maple syrup, powdered sugar, and vanilla extract until smooth.
Once the rolls are done, let them cool slightly before drizzling the maple glaze over the top. Serve warm.