Sift together flour, baking powder, and baking soda, and set aside. Using a handheld mixer, beat the butter, 1-1/4 c. sugar, and salt on high speed until light and fluffy, 4-5 minutes. Reduce the speed to low and beat in the eggs one at a time.
Combine the milk and lime juice (it will curdle, and this is OK) in a measuring cup. With the mixer still on low, add the dry ingredients in three parts, alternating each with the milk mixture. Mix in the lime zest. Use a rubber spatula to scrape the bottom and sides. Pour the batter into the prepared pan, spread it evenly with the spatula, and scatter the blueberries over the top. Sprinkle with the remaining tablespoon of sugar.
Bake until the cake is golden brown on top (the blueberries will sink into the batter) and the cake is beginning to pull away from the sides, 50-55 minutes. Let cool in the pan on a wire rack, then turn out, peel the parchment from the bottom of the cake, and invert onto a serving platter. Cut into wedges and serve warm or at room temperature.
Makes 8-10 servings (1 cake).
Adapted from Yankee magazine, June 2021, p. 42.