In a large mixing bowl, whisk together the warm milk and sugar until dissolved. Sprinkle the yeast over the milk mixture and let it sit for about 5-10 minutes until foamy.

Add the melted butter, eggs, flour, and salt to the yeast mixture. Knead everything together until you achieve a smooth, elastic dough. If the dough feels sticky, add a bit more flour gradually.

Place the dough in a greased bowl, cover it with a clean kitchen towel, and let it rise in a warm environment for about an hour, or until it doubles in size.

While waiting, melt the butter in a skillet over medium heat. Add the apples, cinnamon, brown sugar, and lemon juice. Cook for about 5 minutes until the apples soften. Let this mixture cool.

Once the dough has risen, punch it down and roll it out into a rectangle (about 18 by 24 inches). Spread the cooled apple mixture evenly over the surface.

Roll the dough tightly, starting from one long side. Slice the roll in half lengthwise to reveal the filling. Twist the two strands together, creating a beautiful braid.

Place the twisted dough into a greased loaf pan. Cover it again with the towel and allow it to rise for another 30-45 minutes until puffy.

Preheat your oven to 350°F (175°C). While the oven heats, prepare the topping by combining sugar, flour, cinnamon, and nuts in a small bowl. Sprinkle this mixture generously on top of the babka before baking. Bake for about 35-40 minutes or until golden brown and a toothpick inserted comes out clean.

Let the babka cool in the pan for about 10 minutes, then transfer it to a wire rack to cool completely. Slice and serve warm to enjoy the gooey apple filling.