Heat the oven to 350°F (175°C). Grease a 9-inch round cake pan or 8-inch square baking pan thoroughly, paying special attention to the bottom and corners, and line the bottom with parchment paper if desired.

Melt 1/4 cup unsalted butter in the prepared pan or in a small saucepan. Sprinkle the packed light brown sugar evenly over the melted butter.

Arrange the 2 cups of fresh blackberries in an even layer over the brown sugar. If the berries are unusually wet, lightly toss them with the optional 1 tablespoon of all-purpose flour first.

Whisk together the flour, baking powder, and salt in one bowl. In a separate bowl, cream the softened butter and granulated sugar until light and fluffy, about 2–3 minutes.

Beat the egg and vanilla into the butter mixture. Add the dry ingredients in two or three additions, alternating with the milk, and mix only until combined.

Carefully spoon the batter over the blackberries and gently spread it into an even layer. Bake for 40–45 minutes, until golden and a toothpick inserted into the cake portion comes out clean or with a few moist crumbs.

Cool the cake in the pan for about 10 minutes. Run a knife around the edge, place a serving plate over the pan, and invert the cake in one confident motion before removing the pan and replacing any berries that remain behind.