Position an oven rack in the middle of the oven and preheat to 350°F (175°C).

Place 4 tablespoons of butter in an 8-inch square cake pan. Put the pan in the oven until the butter melts, about 4 minutes.

Remove the pan from the oven and sprinkle the 4 tablespoons brown sugar evenly over the melted butter.

Arrange the peach slices in overlapping rows so the bottom of the pan is evenly covered.

In a medium bowl, whisk together the flour, baking powder, baking soda, cinnamon, and salt until well combined.

In a large bowl, beat the remaining 8 tablespoons butter and granulated sugar with an electric mixer on medium-high speed until well blended, about 3 minutes.

Add the eggs one at a time, beating on medium speed until just combined. Add the lemon zest with the second egg.

Using a spatula, fold the dry ingredients and the buttermilk alternately into the butter mixture, beginning and ending with the dry ingredients.

Spoon the batter into the prepared pan and spread it evenly over the peaches.

Bake until a toothpick inserted in the center comes out clean, about 40–50 minutes.

Let the cake cool in the pan for 10 minutes, then invert it onto a wire rack or serving plate to cool slightly.

Serve warm or at room temperature.