Step 1: In a large bowl, whisk together the warm milk, sugar, and yeast. Let sit for 5-10 minutes until foamy.
Step 2: Add the melted butter, egg, salt, and half the flour. Mix until combined, then gradually add the remaining flour until a soft dough forms.
Step 3: 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 1.5 hours.
Step 4: While the dough rises, melt 1 tbsp butter in a skillet over medium heat. Add the diced pears, brown sugar, 1 tsp cardamom, and cinnamon. Sauté for 5-7 minutes until pears are tender and the liquid has thickened. Let cool completely.
Step 5: Punch down the risen dough and roll it out into a 12x18 inch rectangle on a floured surface.
Step 6: Spread the cooled pear mixture over the dough, leaving a 1-inch border. Sprinkle the remaining 0.5 tsp of cardamom over the fruit.
Step 7: Roll the dough tightly from the short end and place it into a greased 9x5 inch loaf pan. Cover and let rise for another 45 minutes.
Step 8: Preheat oven to 350°F (175°C). Bake the loaf for 35-40 minutes until golden brown and it sounds hollow when tapped. Cool in the pan for 10 minutes before transferring to a wire rack.