Activate the yeast: In a large mixing bowl or stand mixer with dough hook, combine warm milk and yeast. Sprinkle in 1 tablespoon of the sugar and let sit for 5 minutes until foamy and bubbly on top. If it doesn't bubble up after five minutes, your yeast is spent — start over.
Mix the dough: Add the remaining ⅓ cup sugar, eggs, melted butter, and lemon zest to the yeast mixture. Mix on low until combined (about 1 minute), then increase to medium speed and add flour gradually, one cup at a time, mixing after each addition. Once all flour is in, knead for about 6-7 minutes until the dough is smooth, slightly tacky but not sticky, and springs back when gently pressed with your finger. If it's sticking badly to your hands, add flour one tablespoon at a time; if it looks dry and crumbly, add water one teaspoon at a time.
First rise: Form the dough into a ball and place in a lightly oiled bowl. Cover loosely with plastic wrap or a damp kitchen towel. Let rise in a warm spot for 60-75 minutes, until doubled in size. You should be able to see the dough pushing up against the sides of the bowl.
Prepare the apple mixture: While the dough rises, mix grated apples with lemon juice to prevent browning. In a separate small bowl, combine softened butter, brown sugar, cinnamon, nutmeg, and cardamom until it forms a thick paste.
Shape the bread: Punch down the risen dough on a lightly floured surface. Roll it out into an 18x12-inch rectangle. Spread the apple mixture evenly across the entire surface of the dough, then spread the brown sugar-spice butter over top. Starting from one long edge, roll the dough up tightly like a jelly roll and pinch the seam to seal.
Second rise: Place the rolled loaf seam-side down on a parchment-lined baking sheet. Cover loosely again and let rise for 40-50 minutes until puffy and nearly doubled (the loaf should look fat rather than flat).
Score and bake: Preheat oven to 350°F while bread rises. Brush the top generously with egg wash, then use a sharp knife or razor blade to score diagonal lines across the top at about one-inch intervals — this helps it brown evenly and gives that classic challah look. Bake for 45-50 minutes until the loaf is deep golden-brown and sounds hollow when you tap the bottom. For extra assurance, an instant-read thermometer should register around 190°F in the center of the loaf.
Cool: Let cool on a wire rack for at least 20 minutes before slicing (rushing this step leaves gummy spots). The bread is best eaten within two days but can be wrapped tightly and frozen for up to three months — slice it before freezing so you only thaw what you need.
