Preheat the oven to 350°F / 175°C. Grease a 9-inch round cake pan and line the bottom with parchment paper. Place the cake pan on a rimmed baking sheet.

In a small saucepan over medium-low heat, melt 2 tablespoons butter. Stir in the brown sugar until smooth.

Pour the brown sugar mixture into the prepared cake pan and spread it evenly over the bottom.

In a medium bowl, gently toss the blackberries with lemon juice. If using frozen blackberries, toss them with cornstarch as well.

Arrange the blackberries in an even layer over the brown sugar topping. Set aside.

In a medium bowl, whisk together the flour, baking powder, and salt.

In a large mixing bowl, beat the softened butter and granulated sugar for 2 to 3 minutes, until light and fluffy.

Add the eggs one at a time, mixing well after each addition. Mix in the vanilla extract and lemon zest.

Add half of the flour mixture and mix on low speed just until combined. Add the milk and mix briefly. Add the remaining flour mixture and mix only until no dry flour remains.

Spoon the cake batter gently over the blackberries. Spread it into an even layer without disturbing the fruit.

Bake for 35 to 40 minutes, or until the cake is golden and a toothpick inserted into the cake portion comes out clean or with a few moist crumbs.

Let the cake cool in the pan for 15 minutes. Run a knife around the edge of the pan.

Place a large serving plate over the cake pan. Carefully invert the cake onto the plate, then lift off the pan.

Serve warm or at room temperature with whipped cream or vanilla ice cream.