Preheat oven to 350°.
To prepare pears, melt 2 tablespoons butter in a small nonstick skillet over medium heat. Add brown sugar and 1/4 teaspoon cardamom; cook 3 minutes or until sugar dissolves, stirring constantly. Pour sugar mixture into a 9-inch round cake pan coated with cooking spray. Arrange pears in an overlapping circle over sugar mixture; set aside.
To prepare cake, lightly spoon flour into dry measuring cups; level with a knife. Sift together flour, baking powder, 1/4 teaspoon cardamom, and salt in a large bowl, stirring well. Place granulated sugar and 1/4 cup butter in a large bowl; beat with a mixer at medium speed until well blended. Add eggs; beat until blended. Add flour mixture to egg mixture alternately with milk, beginning and ending with flour mixture. Stir in vanilla. Spoon batter into center of prepared pan; gently spread batter to cover fruit.
Bake at 350° for 50 minutes or until a wooden pick inserted in the center comes out clean. Cool in pan 10 minutes on a wire rack; run a knife around outside edge. Place a plate upside down on top of pan; invert onto plate. Let stand 2 minutes before removing pan. Cut into wedges.