Step 1: In a large bowl, combine the warm milk, granulated sugar, and yeast. Let it sit for 5-10 minutes until foamy.
Step 2: Whisk in the melted butter and egg until well combined.
Step 3: Gradually add the flour, 1 tsp cardamom, and salt. Stir until a shaggy dough forms.
Step 4: Knead the dough on a floured surface for 8-10 minutes until smooth and elastic. Place in a greased bowl, cover, and let rise in a warm place for 1 hour.
Step 5: While the dough rises, prepare the filling by combining diced pears, brown sugar, 1 tbsp cardamom, cinnamon, and lemon juice in a saucepan over medium heat. Cook for 5 minutes until pears soften and liquid reduces. Let cool completely.
Step 6: Punch down the risen dough and roll it into a 12×18 inch rectangle on a lightly floured surface.
Step 7: Spread the cooled pear filling evenly over the dough, leaving a 1-inch border.
Step 8: Roll the dough tightly from the long edge into a log and pinch the seam to seal.
Step 9: Place the log in a greased 9×5 inch loaf pan. Cover and let rise for another 30-45 minutes.
Step 10: Preheat oven to 350°F (175°C). Brush the top of the loaf with egg wash.
Step 11: Bake for 30-35 minutes or until the top is golden brown and the internal temperature reaches 190°F.
Step 12: Remove from the oven and let cool in the pan for 10 minutes before transferring to a wire rack.