In a large bowl) whisk together 2 cups of the flour (250g), sugar, yeast, and salt. Set aside.
Whisk together the eggs and set aside.
In a small saucepan, melt together milk and butter until butter has just melted. Remove from the heat and add water and vanilla extract. Let mixture stand for a minute or two, or until the mixture is room temperature or registers 46-50 C (115 to 125 degrees F) on a thermometer.
Pour the milk mixture into the dry ingredients and mix with a spatula or with the dough hook on your stand mixer. Add the eggs and stir the mixture until the eggs are incorporated into the batter. It might take some time to come together but that's fine. Keep stirring!
Add 3/4 cup of flour (94g) and continue mixing (either with spatula or dough hook in mixer) for about 2 minutes. The dough will come together and feel sticky which is the correct texture.
Place the dough is a large bowl that has been lightly greased with oil. Cover with plastic wrap or a damp kitchen towel. Place in a warm space and allow to rest until doubled in size, about 1 hour.* Follow note for make ahead instructions.
While the dough rises, whisk together the sugar, cinnamon and nutmeg for the filling. Set aside.
Brown the butter by heating in a saucepan over medium heat and whisking while the butter changes color to a golden brown, and little brown flecks begin to form.** Set butter aside.
Grease a 9x5 inch loaf pan, and dust with flour. Set this aside.
Once dough has risen for about 1 hour, deflate the risen dough, and knead in an additional 2 tablespoons of flour. This will make it less sticky. Cover again and let it rest 5 minutes.
On a lightly floured work surface, use a rolling pin to roll the dough out. The dough should be 12-inches tall and about 20-inches long. It'll form a long thick rectangle. Roll it out as big as you can get.
Use a pastry brush to spread the cooled brown butter all over the dough rectangle, leaving just a 1-2 inch of dough border around the sides.
Sprinkle the top of the browned butter with the whole cinnamon sugar mix, even though it seems like a lot go for it!
Using a very sharp knife or a pizza cutter, slice the dough vertically into 6 equal sized strips from top to bottom. Stack these six slices on top of each other, and cut again into six squares.
Place these squares accordion like into the prepared loaf pan (So they are all on their sides). Place the damp kitchen towel over the loaf pan, and allow to rise again in a warm place for 30-45 minutes. Heat the oven to 180 C (350 F) while the dough rises.
Once resting period is over, bake the dough for 30-35 minutes or until a deep golden brown. Don't under bake or bread will be cooked on top but doughy in the middle.
Remove from the oven, allow to rest for 15-20 minutes, then run a knife around the edges of the pan and flip the loaf out onto a serving platter. Enjoy immediately while warm! (Although leftovers can be kept for 2 days at room temperature and reheated).