Heat milk and butter for 60-90 seconds in a microwave safe bowl. Add the salt, then set aside to cool until just warm (about 120° to 130°F).
1 cup milk, 1/4 cup salted butter, 1 1/2 teaspoon salt
In a separate bowl, combine the warm water, about 1 tablespoon of the sugar, and the yeast. Stir, then let it sit for 5-10 minutes until the yeast is foamy.
2/3 cup warm water, 1/2 cup granulated sugar, 1 Tablespoon active dry yeast
Once the yeast is foamy, add the milk and butter, the remaining sugar, eggs, vanilla extract, and 1 cup of the flour. Mix well, then continue adding flour while kneading with the dough hook attachment, 1 cup at a time. Only add the additional 1/2 cup of flour if the dough is really sticky.* Knead for 5 minutes on medium speed or 8-10 minutes by hand to create a very soft dough that starts coming away from the sides of the bowl.
2 large eggs, 2 teaspoons vanilla extract, 5 to 5 1/2 cups all-purpose flour
Turn out the dough onto a floured surface and knead a few times by hand until a smooth, round ball forms. Clean and lightly oil the bowl, then return the dough to the bowl, turning to coat. Cover with plastic wrap and let rise in a warm place for 1-2 hours until doubled in size.