Make the dough. In a large bowl, whisk flour, sugar, yeast, and salt.
Add lukewarm milk, eggs, and vanilla. Mix until a shaggy dough forms. Knead by hand or with a mixer (dough hook) for 3–4 minutes until smooth.
Add the butter. Knead in the softened butter, 1 tablespoon at a time, until fully incorporated.
Continue kneading 6–8 minutes more, until the dough is elastic and slightly tacky but not sticky. If needed, dust with 1–2 tablespoons flour to keep it manageable.
First rise. Form a ball, place in a lightly greased bowl, cover, and let rise in a warm spot until doubled, about 1–1.5 hours. If your kitchen is cool, allow extra time.
Cook the apples. While the dough rises, melt butter in a skillet over medium heat.
Add diced apples, brown sugar, cinnamon, nutmeg, lemon juice, and a pinch of salt. Cook 5–7 minutes until the apples soften and the juices thicken. Stir in apple butter if using.
Cool completely.
Prepare the pan. Grease a 9×5-inch (23×12 cm) loaf pan and line with a parchment sling for easy removal.
Roll the dough. Turn the risen dough onto a lightly floured surface. Roll into a rectangle, about 12×16 inches (30×40 cm). Aim for even thickness.
Spread the filling. Spread the cooled apple mixture evenly over the dough, leaving a 1/2-inch border on all sides to prevent spillover.
Roll it up. Starting from a long side, roll the dough into a tight log.
Pinch the seam to seal. Trim the ragged ends if needed.
Make the twist. Using a sharp knife, slice the log lengthwise to expose the layers. With the cut sides facing up, gently twist the two strands together, crossing them several times.
Tuck the ends under.
Pan and proof. Lift the twist into the prepared pan. Cover lightly and let rise until puffy, 35–55 minutes. The dough should rise close to the rim.
Preheat and bake. Preheat the oven to 350°F (175°C).
Bake 35–45 minutes, until deep golden and the internal temperature hits about 190°F (88°C). If the top browns too quickly, tent with foil for the last 10–15 minutes.
Make the syrup. While the babka bakes, simmer water and sugar until dissolved, 2–3 minutes. Remove from heat and stir in vanilla.
Glaze and cool. When the loaf comes out, immediately brush the hot babka with the warm syrup until it’s glossy.
Cool in the pan 15 minutes, then lift out and cool on a rack at least 1 hour before slicing.