So first you're gonna make some caramel. Put 3/4 cup sugar and 1/2 cup water in a small saucepan. Swirl it to get all the sugar moistened. Bring to a boil over high heat and then DONT EVEN THINK ABOUT TOUCHING IT until it starts turning golden around the edges. Then start slowly swirling the pan occasionally to caramelize the sugar evenly until it's all golden brown and, well, caramel-colored. Turn down the heat to low, then whisk in the soft butter. Careful it doesn't splatter and burn you! Season with a little pinch of salt.
Stir the pineapple into the pot. You can now transfer it to a bigger pot. Cook on medium-low, simmering until the pineapple is nice and golden brown, 8-10 minutes. You'll get little bits of hardened caramel--no worries! It'll melt back into the sauce.
Take the fruit out with a slotted spoon. Then turn up the heat to med-high and reduce the liquid until syrupy. Pour into a buttered 9" cake pan. Arrange pineapple so the whole bottom is covered. Now prepare your cake batter.
Sift the flour, baking powder, and salt into a bowl. In another bowl, whisk your 3 egg yolks with the 2 whole eggs. Then whisk in the sugar, the cooled melted butter, and vanilla.
With a spatula, fold in the wet ingredients to the dry ingredients just to incorporate. Pour evenly over the pineapple then bang it on the counter several times to get any air bubbles out. Bake it in a 350 degree oven for about 50 minutes until golden brown and bubblin around the edges.
Cool in the pan set on a metal rack for 30 minutes. Invert onto a cake plate or cutting board. If pineapple falls off just stick it right back on there! Serve warm or let cool to room temperature. Best with vanilla bean ice cream. Or salted caramel ice cream. Or bourbon pecan ice cream...k i'll shut up and you go eat some cake!