Wash, halve, and pit the plums. Cut them into quarters.
Preheat oven to 350°F. Grease a deep baking sheet with butter and dust it with breadcrumbs.
Cream together butter, sugar, vanilla extract, and salt. Beat in the eggs one at a time.
In a separate bowl, mix flour, baking powder, and cornstarch. Now, incorporate the dry ingredients into the batter.
Spread the batter evenly on the baking sheet and arrange the plum pieces densely on top.
Mix the egg yolks with sugar and cinnamon and pour the mixture over the plums.
Bake the cake for 50 minutes and let it cool afterward.
Serve plain or with a dollop of whipped cream.