Pineapples symbolize luck and wealth and thus are very popular during Lunar New Year. The word for pineapple in some Chinese dialects sounds like prosperity.
Technique tip: The caramel can be made ahead for the cake, the pineapple cut, the dry ingredients and wet ingredients fully measured out so it's a very easy pull together on the day of. You can also make this cake in advance and serve it the next day.
Using a serrated knife, peel, halve, core and slice the pineapple into 3/4-inch-thick slices. Cut these slices in half.2.
Carefully place the sugar in the bottom of the pan. Add the water to the sugar and gently swirl the pan to moisten the sugar; if necessary poke your fingers around the bottom of the pan to make sure all of the sugar mixes with the water. Place the saucepan on high heat and leave the pan undisturbed until it comes to a rolling boil. Once it comes to a boil, continue to let it boil rapidly without moving the pan until it starts to caramelize. This will take 3-4 minutes: you'll see the sugar syrup boil furiously, then as it thickens it will boil more languidly until finally around the edge of the pan you'll see some of the syrup starting to color and darken.3.
When you see color in the pan, start to gently swirl in a circular motion so the sugar caramelizes evenly. Continue swirling the pan until the caramel is medium golden brown. Turn the heat down to low and whisk in 6 tablespoons of butter; be careful as the caramel may sputter and steam. Carefully add the pineapple and stir until it is coated with caramel. Don't worry if some of the caramel hardens; it will re-liquify as it continues to cook. Bring it to a boil and then turn heat down to medium-low and let simmer for 8-12 minutes, until the pineapple turns golden brown. The pineapple will release juice and liquefy the caramel. Remove the pineapple from the saucepan with a fork. Continue to boil the remaining liquid on medium-high heat for 2-3 minutes, until the mixture is thick and syrupy.4.
Heat the oven to 350°F and generously butter a 9-inch cake pan.5.
Add all of the pineapple and caramel syrup to cake pan, arranging the pineapple in concentric circles, covering as much of the bottom of the pan as possible. Cut the pineapple halves into smaller pieces to fill in any gaps and double layer the pineapple if there is extra pineapple.6.
Sift the flour, baking soda and salt into a medium bowl. Whisk together the eggs and egg yolks in a large bowl; slowly whisk in the sugar, vanilla extract and the 1/2 cup melted butter. Use a rubber spatula to fold the dry ingredients into the wet ingredients until well combined. Pour the batter over the pineapple in the cake pan and tap the pan gently on a counter to get rid of any air bubbles in the batter and make sure the batter fills in any crevices in the pineapple and settles into the bottom of the pan.7.
Bake for 50-60 minutes, until the cake is golden brown all over and springs back lightly when you poke it in the middle. Remove the cake from the oven and let cool for about 30 minutes, until cool enough to handle. Place a serving plate upside-down on top of the cake pan and carefully invert the cake pan onto the plate, holding them tight together. Remove cake pan from the cake. If some of the pineapple sticks to the pan, remove it and re-arrange it on top of the cake. Let the cake cool for at least another 30 minutes and serve warm or at room temperature. The cake may be stored in an airtight container at room temperature for up to 2 days.