In a bowl or measuring cup, stir 1 teaspoon granulated sugar into the warm milk. Gently stir in the active dry yeast. Living yeast will foam up and give off a smell after about 5-10 minutes.
While the yeast is proofing, cream together the butter and sugar in your stand mixer using the paddle attachment on medium speed. You're looking for the color to be light yellow and the sugar and butter are mixed together completely.
Add the vegetable oil and vanilla extract on low speed, then add egg yolks one at a time, beating each one in before the next addition. Mix on a medium-low speed for another 2-3 minutes.
On low speed, add 2 ½ cups all-purpose flour and 1 teaspoon kosher salt. Give your yeast-milk mixture a quick whisk before adding it into the stand mixer as well.
Mix until the flour is just combined, then replace the paddle attachment with your dough hook. Knead with your dough hook, adding 1 tablespoon of flour at a time, just until the dough comes together. The amount of flour you need will be based on humidity and altitude, so gradually add the flour and check the texture of the dough. It should be soft, pliable, and just barely tacky. Watch the dough, it's easy to over-knead in a stand mixer.
Once the dough is soft and can be formed into a ball easily, it should be easy to remove from the dough hook, Transfer it to a lightly floured work surface and knead the dough several times by hand until you have a smooth ball of dough. It's much for difficult to over-knead when it's by hand, but be careful to not over-knead.
Place the ball of dough into a large, oiled mixing bowl and cover it with plastic wrap. Find a warm place to let the dough double in size, like the oven trick or outside if it's a warm day, for about 2-3 hours. It's a rich dough so it'll take a while to rise. While this is rising, line your bread pan in aluminum foil or parchment paper.
Once the dough has risen, plop it onto a lightly floured work surface and roll it out to a large rectangle. Generously smooth all of the apple butter evenly over the dough, leaving an inch border around the dough.
Roll the dough up longways (so it becomes a long log) and then twist the dough into a figure-eight shape. Put the babka dough into the lined bread loaf, cover in plastic wrap, and let rise in your warm space for 1 hour. It should fill the pan almost completely, but it will get huge once it bakes.
Preheat the oven to 350 degrees F (180 degrees C).
Brush the top of the dough with your reserved egg white and a little splash of water.
Place the babka into the preheated oven on the middle rack for 25 minutes, then turn the pan 180 degrees and bake for another 25 minutes.
Let the babka cool for at least an hour before cutting. To store, wrap the loaf in plastic wrap and keep in the fridge for up to 4 days.