Step 1: Preheat your oven to 350°F (175°C). Generously grease and flour a 10-inch (12-cup) bundt pan, ensuring all crevices are covered.
Step 2: In a medium bowl, whisk together the 3 cups of flour, ground cardamom, baking powder, baking soda, and salt. Set aside.
Step 3: In a large bowl or stand mixer, cream the softened butter and granulated sugar together on medium-high speed until light and fluffy, about 3-5 minutes.
Step 4: Add the eggs one at a time, beating well after each addition. Mix in the vanilla extract.
Step 5: Reduce the mixer speed to low. Add the dry ingredients in three parts, alternating with the sour cream in two parts, beginning and ending with the dry ingredients. Mix just until combined.
Step 6: In a small bowl, toss the diced pears with 1 tablespoon of flour. Gently fold the pears into the cake batter using a spatula.
Step 7: Spoon the batter into the prepared bundt pan and smooth the top with a spatula.
Step 8: Bake for 55-65 minutes, or until a skewer inserted into the center comes out clean or with just a few moist crumbs.
Step 9: Allow the cake to cool in the pan for 10 minutes. Then, carefully invert the pear cardamom bundt cake onto a wire rack to cool completely before serving.