In a 10-inch cast-iron skillet, heat oil over medium-high heat. Add half of pineapple; cook until lightly browned, about 1 minute per side (reduce heat to medium, if necessary). Remove from skillet. Add remaining pineapple, and repeat procedure. Remove skillet from heat; let cool for 20 minutes. Wipe skillet clean.
In a medium bowl, whisk together flour, sugar, baking powder, and salt. Pour flour mixture into the bowl of a stand mixer fitted with the paddle attachment. Add milk, butter, and vanilla; beat at low speed until combined, about 1 minute. Increase mixer speed to high. Beat for 2 minutes, stopping to scrape sides of bowl. Reduce mixer speed to low. Add egg yolks, one at a time, beating well after each addition. Spread batter into cooled skillet. Arrange pineapple over batter, overlapping slices. Sprinkle with Brown Sugar Crumble.
Bake until golden brown, 35 to 40 minutes. Let cool for 30 minutes. Drizzle with Brown Sugar- Lemon Glaze before serving.
Recipe by Bake from Scratch at https://bakefromscratch.com/right-side-pineapple-crumb-cake/