In a large mixing bowl, stir together 1 cup of the flour, sugar, and yeast.
In a small saucepan over low heat, melt the butter in the milk until the butter has melted but do not bring to a boil.
Add the milk to the flour and beat at low speed of an electric mixer for two minutes.
Add the eggs, and vanilla beating well.
Add 1 additional cup of flour and beat for two minutes.
Add the remaining 2 ¼ cups flour and beat an additional two minutes. Batter will become sticky against the beater.
Put the dough onto a lightly floured pastry board and knead the dough for 10 minutes, adding flour as necessary to keep it from sticking to the board.
Butter a large bowl, add the dough ball, and butter the top of the dough. Place a towel over the top of the bowl and place in an oven with the light on for one hour.
Butter a large 13" x 9" pan.
Punch down the dough and knead it a few times. Recover with the towel and let it set on the counter for 10 minutes.
On a lightly floured pastry board, roll the dough into a 15" x 12" rectangle.
Brush the 3 Tablespoons of melted butter onto the dough.