Preheat oven to 325°F (170°C). Spray a 9-inch springform pan with baking spray with flour. Line bottom of pan with parchment paper.

In the bowl of a stand mixer fitted with the whisk attachment, beat eggs at high speed until uniform in color and foamy, about 1 minute. With mixer on medium speed, add granulated sugar in a slow, steady stream, beating until combined. Increase mixer speed to high, and beat until thick and pale, about 2 minutes. With mixer on medium-low speed, add oil in a slow, steady stream, beating until combined; scrape sides of bowl. With mixer on medium speed, gradually add milk and vanilla bean paste, beating until combined.

In a medium bowl, whisk together flour, baking powder, and salt. Fold flour mixture into egg mixture just until combined. Pour batter into prepared pan. Gently tap pan on a kitchen towel-lined counter to release any large air bubbles. Top with plum slices, going all the way to edges and overlapping as needed.

Bake until a wooden pick inserted in center comes out with a few moist crumbs, 45 to 55 minutes. Let cool in pan for 15 minutes. Remove sides of pan. Serve warm, or let cool completely on pan base on a wire rack.