In a small saucepan, combine butter and milk and heat on stove over medium heat until butter is just melted. Add vanilla extract and water. Set aside to slightly cool.
In a mixing bowl fitted with the dough hook attachment, whisk together the flour, sugar, yeast and salt. Pour the milk mixture into the dry ingredients and mix on low speed, then add the eggs and mix until the eggs are fully incorporated, about 2 minutes. Add more flour, as needed, until the dough clears the sides of the bowl.
Grease a large bowl and transfer the dough to the bowl, turning once to coat. Cover the bowl tightly with plastic wrap and let rise in a warm area until doubled in size, about 1 hour. (If using an overnight method, at this point, after the dough is risen, you can wrap the dough tightly with plastic wrap and refrigerate overnight to finish in the morning. Allow to rest at room temperature for 30 minutes before proceeding. Otherwise, if you wish to make this all in one day, continue on to the next step.)
After the dough is doubled in size, in a small bowl, combine sugar, cinnamon and nutmeg. Mix and set aside.
Melt the butter for the filling in a small saucepan until slightly browned, making sure not to burn it. Set aside to slightly cool.
Grease and flour a 9x5x3-inch loaf pan. Set aside.
Punch down the dough and turn it out onto a lightly floured work surface. Cover with a clean towel and let rest for 5 minutes. Roll out to a 12- by 20- inch rectangle. (No worries if it won't stretch to 20-inches, just go as large as you can.)
Spread the melted butter across the surface of the dough, then sprinkle evenly with the cinnamon sugar mixture until it is gone.
Slice the dough vertically into six equal sliced strips.
Pile on top of each other.
Slice into six equal sized squares.
Layer the dough slices into the loaf pan like a flip book. Cover with a towel and allow to rise in a warm place for 45 minutes, or almost doubled in size.
Arrange a rack to the center of the oven and preheat to 350 degrees F. Bake the loaf for 30 to 35 minutes, until the top is very golden brown. Remove from the oven and let cool in the pan for 20 to 30 minutes. Run a butter knife around the edges and invert onto a large board, then invert again onto a large serving platter. Serve warm.
This is best the day it's made, but can be stored up to 2 days.