Lemon Cake with Fruit
['1 cup (2 sticks) unsalted butter, room temperature, plus more for pan', '2 cups all-purpose flour, plus more for pan', '2 tsp. baking powder', '1 1/2 tsp. kosher salt', '1 lemon', '1 2/3 cups plus 3 Tbsp. granulated sugar', '3 large eggs', '1 large egg yolk', '3 Tbsp. pear, orange, or apple brandy (optional)', '2 lb. pears or apples, sliced, stone fruit, cut into thick wedges, blueberries, and/or blackberries', 'Powdered sugar (for serving)']
Place a rack in middle of oven and preheat to 350°F. Butter and flour a 13x9" baking pan. Whisk baking powder, salt, and 2 cups flour in a medium bowl. Finely grate lemon zest into another medium bowl. Slice lemon in half; set aside. Add 1 2/3 cups granulated sugar to zest and work with your fingers until mixture is fragrant and looks like wet sand, about 1 minute.
Using an electric mixer on medium speed, beat 1 cup butter in a large bowl until smooth, about 20 seconds. Add sugar mixture, increase speed to medium-high, and beat until very light and fluffy, about 5 minutes. Reduce speed to medium and add eggs one at a time, beating well between additions; mix in egg yolk. Reduce speed to low and gradually add dry ingredients. Beat just until incorporated, then add brandy and beat just until smooth. Fold batter a few times with a rubber spatula; scrape into prepared pan and smooth top. Scatter fruit over (do not press down). Squeeze a reserved lemon half over fruit (save other half for another use) and sprinkle with remaining 3 Tbsp. granulated sugar.
Bake cake until sides are golden brown and top is golden, 55–65 minutes. Let cool; cut into squares. Serve dusted with powdered sugar.
Cake can be baked 2 days ahead. Store tightly wrapped at room temperature.
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