Heat whole milk in a saucepan until lukewarm (about 110°F). Combine half of the sugar with the warm milk and sprinkle in fresh yeast. Let sit for 5-10 minutes until foamy.

In a stand mixer, combine the yeast mixture, egg, egg yolk, bread flour, and salt along with the remaining sugar. Mix on low speed until combined, then knead for 5-8 minutes until smooth and elastic.

Gradually add room-temperature unsalted butter, one tablespoon at a time, kneading for another 10 minutes until shiny and elastic.

Transfer the dough to an oiled bowl, cover with plastic wrap, and refrigerate overnight for about 12 hours.

Prepare the filling by mixing chopped walnuts, granulated sugar, ground cinnamon, and melted butter in a bowl. Let it cool to room temperature.

Roll out the chilled dough into a rectangle (12x18 inches and 1/4 inch thick).

Spread walnut filling over the dough. Roll tightly from one long edge and pinch seams to seal. Cut the log in half lengthwise and twist the two halves together.

Place the shaped dough in a greased loaf pan and cover loosely. Let it rise at room temperature for 1 to 2 hours until doubled in size.

Preheat the oven to 350°F (175°C). Bake the Walnut Babka for 35-40 minutes until golden brown and a toothpick comes out clean.

Make the syrup by simmering water, granulated sugar, and lemon juice in a saucepan for 5 minutes until slightly thickened. Brush over warm babka after baking.