Combine warm milk, yeast, and 1 teaspoon of the sugar in a small bowl. Stir and let sit for 8 to 10 minutes until foamy.

In a large bowl, whisk together flour, remaining sugar, and salt. Make a well in the center and add the yeast mixture and eggs.

Mix until a shaggy dough forms, then turn out onto a lightly floured surface and knead for 5 minutes until smooth.

Add the softened butter a tablespoon at a time, kneading it in fully before adding the next piece. Continue kneading for 6 to 8 minutes until the dough is smooth, elastic, and slightly tacky.

Place dough in a lightly oiled bowl, cover with a clean kitchen towel, and leave to rise at room temperature for 1 hour or until doubled in size.

Toast walnuts in a dry pan over medium heat for 3 to 4 minutes, shaking often, until lightly golden and fragrant. Let cool completely.

Pulse toasted walnuts in a food processor until finely ground. Do not over-process into a paste.

Combine ground walnuts, honey, sugar, lemon zest, and cinnamon in a bowl. Stir until a thick, spreadable paste forms. Add the milk one tablespoon at a time if the mixture seems dry.

Heat the oven to 180 C / 355 F. Grease a 900 g / 2 lb loaf pan with butter and line with parchment paper.

Punch down the risen dough and turn it out onto a lightly floured surface. Roll into a rectangle roughly 40 cm x 30 cm / 16 in x 12 in, about 4 mm thick.

Spread the walnut filling evenly over the dough, leaving a 2 cm border on all sides.

Starting from the long edge, roll the dough into a tight log. Pinch the seam and both ends firmly to seal.

Place the log seam-side down in the prepared loaf pan. Cover loosely and rest for 30 minutes until slightly puffed.

Brush the top evenly with beaten egg. Bake for 38 to 40 minutes until deep golden brown on top and the internal temperature reads 88 C / 190 F.

Remove from the oven and immediately brush the top with warmed honey. Let cool in the pan for 15 minutes, then transfer to a wire rack to cool for at least 30 minutes before slicing.