Preheat oven to 375°F (190°C). Spray a 9-inch square baking pan with baking spray with flour. Line pan with parchment paper, letting excess extend over sides of pan.

In the bowl of a stand mixer fitted with the paddle attachment, beat butter and 1¾ cups (350 grams) granulated sugar at medium speed until fluffy, about 3 minutes, stopping to scrape sides of bowl. Add eggs, one at a time, beating well after each addition. Beat in extracts.

In a medium bowl, whisk together flours, baking powder, salt, and baking soda. In a small bowl, whisk together milk and sour cream. With mixer on low speed, gradually add flour mixture to butter mixture alternately with milk mixture, beginning and ending with flour mixture, beating just until combined after each addition. Carefully fold in 8 ounces (227 grams) blackberries. Spread batter into prepared pan.

Tap pan on a kitchen towel-lined counter several times to spread batter and release any air bubbles. Top batter with remaining 4 ounces (113 grams) blackberries. Sprinkle with remaining 2 tablespoons (24 grams) sugar; sprinkle with almonds.

Bake for 15 minutes. Reduce oven temperature to 350°F (180°C), and bake until a wooden pick inserted in center comes out with a few moist crumbs, 30 to 40 minutes more. Let cool in pan for 10 minutes. Using excess parchment as handles, remove from pan, and let cool completely on a wire rack. Store in an airtight container for up to 3 days.