To make the dough sprinkle the yeast over the warm ⅓ cup water and stir. Wait 5 minutes for the yeast to dissolve. Pour into the mixer bowl. Add the milk, ⅓ cup cold water, sugar, egg yolk and vanilla and whisk to combine.
Fit the mixer with a paddle attachment and on low speed gradually add half of the flour, then the salt. One tablespoon at a time add the butter. Gradually add the remaining flour to form a rough dough. Replace the paddle attachment with a dough hook and knead on medium low speed adding more flour if needed until the dough cleans the bowl. Continue kneading until the dough is soft, smooth and elastic, about 6 minutes.
Transfer the dough to a lightly floured work surface and knead briefly to check the dough’s texture. The dough will be slightly sticky. Butter a large bowl and transfer the dough to the bowl. Cover tightly with plastic wrap and set in a warm place to rise until doubled in volume, about 1 ½ hours.
When the dough has risen prepare the apple filling. Mix the cut apples, egg yolk, sugar and cinnamon in a medium bowl.
Butter two 8 ½-by-4 ½-by-2 ½-inch loaf pans. Line the bottoms with parchment paper and dust the sides with flour. Set aside.
Place the dough on a lightly floured work surface. Roll or stretch the dough into a 16-by-12-inch rectangle. Spread the filling over the dough and starting at the top begin to roll up the dough, jelly roll style.
Using a bench scraper or large knife, cut the dough into 1-inch-thick slices.
Now cut through the slices to make 1-to-1 ½-inch pieces. It will look like quite a mess, but you’re doing the right thing. Using the bench scraper, scoop up the dough-apple mixture and divide equally among the prepared loaf pans (a kitchen scale comes in handy here), distributing as evenly as possible.
Choose a warm spot in your kitchen for proofing the loaves. Place the pans on a cookie sheet. Fill a glass with very hot water. Place the pan with the loaves inside a big plastic garbage bag, place the glass of hot water in the bag, inflate the bag by waving the opening up and down, then close tightly. This will mimic a professional proofing oven (you can also just set the pans in a warm place; this worked fine for me).
Let stand until the loaves have risen to the top of the pans (mine actually puffed up much higher than the edge of the pans), about 1 hour. The dough will look lumpy.
Preheat the oven to 350°F. Remove the glass from the pan, then the pan from the bag. Bake on the center rack (on the cookie sheet) for 30 to 35 minutes. Cover the loaves loosely with foil and bake for another 25 to 30 minutes or until the tops are golden brown and an instant read thermometer reads 210°F.
Transfer the loaf pans to a wire cooling rack and let stand for 5 minutes. Unmold the loaves onto the rack. Remove the parchment paper and turn the loaves right sides up and let cool completely.