Position an oven rack in the lower third of the oven. Preheat the oven to 350°F (177°C). Set aside an 8-inch or 9-inch cake pan that is at least 2 inches tall.

Remove the ends and peel the pineapple. Cut into four long wedges, and then cut away the core. Slice two of the wedges into ½-inch thick slices.

Spread 4 tablespoons of the butter over the bottom of the cake pan. Scatter the brown sugar and cinnamon evenly over the butter. Arrange the pineapple wedges in one even layer over the butter and sugar.

In a large bowl, beat the remaining 8 tablespoons of butter, granulated sugar, and zest with an electric mixer on high speed until light and fluffy, 2 to 3 minutes.

Add the egg yolks and vanilla and beat until smooth. Save egg whites for later.

In another bowl, whisk or sift the flour, baking powder, and salt together.

On low speed, mix half of the flour mixture into the butter and egg yolk mixture until only a few streaks of flour remain, then mix in the remaining flour.

Add the (unbeaten) egg whites and sour cream. Mix on low speed until blended.

Spoon the cake batter onto the pineapple in the pan, then spread it into an even layer. Bake until a toothpick inserted in the center of the cake comes out clean, 35 to 40 minutes.

Cool the cake in the pan for 5 minutes, then run a knife around the edges and invert it onto a plate to cool.

If some pineapple slices stick to the pan, use a spatula to transfer them back on top of the cake, then spread some gooey brown sugar sauce over them to cover them up. Serve warm or at room temperature.