Start the dough: Combine the milk and sugar in the bowl of a stand mixer, then sprinkle the yeast over the milk and set aside to proof for about 5 minutes or until bubbles form on the surface of the milk.
Add the egg, honey, and vanilla. Mix on low speed using the paddle attachment for about 30 seconds until combined. Add the flour, and the salt and mix on low speed until the flour is incorporated into the liquid and a sticky dough forms. Add the butter, 1 tablespoon at a time, waiting until it is incorporated before each addition.
Once all the butter is added, switch to the dough hook and knead the dough on medium-high speed until a smooth and slightly sticky dough forms, about 5 minutes. Gather the dough into a ball, stretching the dough so the top of the ball is smooth. Grease a bowl with a light coating of canola oil or butter, then place the dough back into the bowl, with the gathered rough part of the dough down and the smooth surface of the ball facing up. Cover with plastic wrap and let rise for about 1 hour, or until the dough has doubled in size. Punch down dough, return to bowl, and chill for at least 1 hour (can rest overnight).
Make the Filling: Melt butter in a large skillet over med-high heat. Cook apples in butter until starting to soften (about 5-7 minutes), then add honey, boiled apple cider, and vanilla.
Reduce heat and simmer until sauce has thickened, 8-10 minutes. Transfer to a bowl and chill for at least 30 minutes in the refrigerator. (Can be made up to 5 days ahead, just bring to room temperature before using).
Shape and bake the babka: Coat a standard loaf pan with cooking spray and line with parchment paper, leaving an 2-inch overhand on the long sides. Set aside.
Dust a clean surface with flour and roll the chilled dough out to a rectangle roughly 10- x 14-inches (about 1/4-inch thick with a long side facing you (landscape orientation). Using an offset spatula, spread the cooled apples over the surface of the dough, leaving a 1-inch strip bare along the long side away from you.
Tightly roll the dough up from the long side facing you, making a 14-inch rope. Chill the rope for at least 30 minutes (chilling helps the dough hold its shape while you twist it).
Slice the rope in half lengthwise using a bench scraper, making two 14-inch long pieces. Twist each long piece individually so the apples are trapped inside the dough, tucking in any apples that may have fallen out. Twist and wrap the two ropes of dough together. Squish the twisted dough together and transfer it to the prepared loaf pan, tucking in any stray pieces of apples and dough. This is messy business but worth it in the end!
Brush the beaten egg over the top of the dough in the pan, then cover with a piece of greased plastic wrap and let rest for 30 minutes.
Adjust the oven rack to the lower third position. Place a baking sheet on the lower rack to catch any drips. Preheat the oven to 350°F (177°C).
Once the dough has rested (it won’t have risen much, just a tiny bit), brush with beaten egg again.
Bake for 55-65 minutes, or until the top of the dough is deep golden brown, the center is firm, and the loaf sounds hollow when tapped on the top (the internal temperature should be above 190°F). If you find the top of the loaf is browning too quickly as it bakes, tent it with aluminum foil...I placed foil on top after about 25 minutes.
Let babka cool in the pan for 15 minutes on a wire cooling rack, then use the parchment paper to lift the babka out of the pan and transfer it to back to the wire cooling rack. Let cool.
Make the glaze: Melt the butter and boiled apple cider together In a small saucepan over low heat, whisking occasionally. Once the butter has melted, remove from heat and whisk in the sifted powdered sugar.
Drizzle the glaze over the babka just before serving, letting it set about 5 minutes (if you can wait that long!). Serve & enjoy!