In a small bowl, mix warm milk, yeast, and 1 tbsp sugar. Let sit for 10 minutes until frothy. (If the yeast doesn’t bloom, restart with fresh yeast.)
Preheat oven to 170°F (or the warm setting) to create a proofing environment.
In a stand mixer, combine 3½ cups flour, melted butter, vanilla, and sugar. Start mixing on low speed.
Slowly add in the milk mixture while mixing.
Add eggs one at a time, ensuring each is fully incorporated.
Increase to medium speed and knead for 5 minutes (or knead by hand for 6 minutes on a floured surface). The dough should be smooth and slightly bouncy.
Form the dough into a ball and place it in a greased bowl. Cover with a kitchen towel or plastic wrap.
Let the dough rise in a warm spot for 1 hour (using the oven trick) or 1½ hours at room temperature.