Preheat oven to 350°F (180°C). Spray a 9-inch round cake pan with baking spray with flour. Line bottom of pan with parchment paper.
Halve and core 6 ounces (170 grams) pears, and chop into small pieces. Halve, core, and slice remaining pears into ⅛-inch-thick slices.
In the bowl of a stand mixer fitted with the paddle attachment, beat butter and 1¼ cups (250 grams) sugar at medium speed until fluffy, 3 to 4 minutes, stopping to scrape sides of bowl. Add eggs, one at a time, beating well after each addition. Beat in vanilla.
In a medium bowl, whisk together flour, baking powder, and salt. With mixer on low speed, gradually add flour mixture to butter mixture alternately with sour cream, beginning and ending with flour mixture, beating just until combined after each addition. Fold in diced pears and 1½ tablespoons (34.5 grams) ginger.
In another medium bowl, combine pear slices, 1 cup (240 grams) water, and lemon juice; let stand for 5 minutes. Remove pear slices, and pat dry with a clean towel.
Spread batter into prepared pan. Shingle pear slices on top of batter; sprinkle with remaining 1½ tablespoons (34.5 grams) ginger, slightly pressing pears into batter. Sprinkle with remaining 1 tablespoon (12 grams) sugar.
Bake until a wooden pick inserted in center comes out clean, 1 hour to 1 hour and 10 minutes, covering with foil to prevent excess browning, if necessary. Let cool in pan for 10 minutes. Remove from pan, and let cool completely on a wire rack.