Position a rack in the center of the oven and preheat the oven to 350ºF (177ºC). For a convection oven, reduce cooking temperature by 25ºF (15ºC). Generously butter a 9-inch (23 cm) round cake pan.
Peel, halve, and core the pineapple, then cut into ¾ inch (2 cm) thick slices. Cut the slices in half. I used this pineapple slicer, which cores and slices an entire pineapple.
Put ¾ cup (150 g) sugar and the water in a medium saucepan and mix well so the sugar is moistened.
Place the pan over high heat and leave it undisturbed. The liquid starts to boil slowly for the first minute or two, and then it will boil rapidly after that. DO NOT TOUCH the pan until the sugar syrup starts to caramelize from the edge of the pan. When you see dark color syrup around the edge of the pan, gently swirl the pan in a circular motion so the sugar caramelizes evenly. Keep swirling gently until the caramel is a medium golden brown.
When it’s medium golden brown, turn down the heat to the lowest and whisk in the 6 Tbsp. butter. Quickly mix well and be careful for splutter.
Carefully add the pineapple and stir until it is coated with the caramel. The caramel will become liquid again once you heat it up and the pineapple will also release juice.
Turn up the heat to medium-high and bring to a boil. By this time you see caramel is re-liquefying already. Then turn down the heat to medium-low and simmer for 10 to 12 minutes, or until the pineapple turns golden brown.
Using a fork, transfer the pineapple to a plate.
Continue to boil the remaining caramel on medium-high heat for few minutes, or until thick and syrupy.
Arrange the pineapple in concentric circles in the prepared pan. Make sure to fill in any gaps at bottom of the pan with smaller pieces. My pineapple was just large enough to cover the bottom (so don’t eat your pineapple until you finish this step!). If you have extra pineapple, you can do double layers. Then pour the caramel syrup on top.
In a medium bowl, sift together the flour, baking powder, and salt.
In a large bowl, beat together the eggs and egg yolks until blended, then slowly beat in the remaining 1 cup (200 g) sugar, the vanilla, and the ½ cup melted butter. Using a rubber spatula, fold the flour mixture into the egg mixture until it's completely mixed.
Pour the batter evenly over the pineapple in the cake pan. Tap the pan gently on a counter top to get rid of any air bubbles in the batter.
Bake at 350ºF (177ºC) for 50 to 60 minutes, or until the top is golden brown. If it becomes golden brown too quickly and not done baking yet, cover with aluminum foil so it doesn't burn. The cake is ready when you insert a skewer in the center of the cake and it comes out clean (batter free). Let cool in the pan on a wire rack for about 30 minutes.
Place a serving plate upside down on top of the cake pan, then holding the pan and the plate tightly together, invert them quickly (but carefully). Lift off the cake pan. If some of the pineapple are stuck to the pan, remove them and place them back on top of the cake. Let the cake cool for at least another 30 minutes, then serve warm or at room temperature.
To Store
The cake can be stored in an airtight container and store at room temperature for up to 2 days and in the freezer for a month.
Notes
The recipe is adapted from Green Cilantro, originally from Joanne Chang's Flour.