Bring 4 cups water and granulated sugar to a boil in a medium saucepan. Add pears; reduce heat to medium, and cook at a medium-low boil for 5 minutes or just until pears start to soften. Remove pears from pan; cool slightly. Trim bottom off each pear so that it is about the height of a 9 x 5–inch loaf pan. Lightly brush 11/2 teaspoons flour over bottom 2/3 of each pear.
Weigh or lightly spoon 7.88 ounces (about 1 3/4 cups) flour into dry measuring cups; level with a knife. Combine flour, baking soda, baking powder, and salt, stirring well with a whisk. Place butter and brown sugar in a large bowl; beat with a mixer at high speed until well blended. Add eggs, 1 at a time, beating well after each addition. Beat in vanilla. Combine beer, sour cream, and syrup, stirring well with a whisk. Beating at low speed, add flour mixture and beer mixture alternately to the butter mixture, beginning and ending with flour mixture; beat just until combined.
Scrape batter into a 9 x 5-inch metal loaf pan coated with baking spray. Arrange pears in pan, pressing into batter. Bake at 350° for 50 minutes or until a wooden pick inserted in the center comes out with moist crumbs clinging. Cool 10 minutes in pan on a wire rack. Remove from pan; cool completely on wire rack.