3/4 cup water
1 tablespoon active dry yeast
3/4 cup whole milk
4 large eggs
1 large egg yolk
3/4 cup sugar
1 1/2 teaspoons salt
1 1/2 teaspoons vanilla extract
6 1/4 - 6 1/2 cups all-purpose flour
12 tablespoons unsalted butter, softened to room temperature
For the sticky filling:
2 1/4 cups pecans
3/4 cups butter (salted)
1 1/2 cups packed dark brown sugar
3 teaspoons cinnamon
For the egg wash:
1 large egg yolk
1 tablespoon whole milk or cream
Make the dough: Combine the water and the yeast in the bowl of a stand mixer, and let stand until the yeast is dissolved. Add the milk, eggs, yolk, sugar, salt, and vanilla extract, and whisk until the yolks are completely combined. Add 6 1/4 cups of flour and stir with a stiff spatula until a shaggy, floury dough is formed.
Using a dough hook, knead on medium-low speed until the dough comes together and is no longer floury, about 5 minutes. With the mixer still running, begin adding the butter in 1-tablespoon blobs. Mix until one blob is just barely incorporated before adding the next blob.
When all the butter has been added, continue kneading for another 5 minutes until the dough is silky, elastic, and quite jiggly. This won't form a ball like regular dough — it should bunch around the dough hook and clear the sides of the dough hook, but will still be attached in a sticky dough mass to the bottom of the bowl. Add the extra 1/4 cup of flour as needed if the dough is sticking to the sides of the bowl. (For step-by-step instructions, see steps 2 through 6 in How To Make Kugelhopf.)
Chill the dough: Transfer the dough to your largest mixing bowl. Cover and let rise for 1 to 1 1/2 hours, until doubled in bulk. Transfer to the fridge and chill for at least an hour or up to 3 days. (This makes the dough easier to roll out in the next step; I recommend letting the dough chill overnight.)
Prepare the filling: When you're ready to shape the loaves, prepare the filling before you take the dough out of the fridge. Heat the oven to 350°F and toast the pecans until they're a few shades darker and very fragrant, about 10 minutes. Transfer the hot pecans to a cutting board and chop them finely while still warm. Keep chopping until no piece is larger than a grain of barley. You can also do this in a food processor — process the nuts in pulses and be careful of over-processing (which will turn the nuts into nut butter!).
In a medium bowl, mash together the softened butter,