Preheat oven to 350 degrees F. Butter the bottom and sides of a 9-inch round cake pan. Line the bottom of the pan with parchment paper.
Add powdered sugar and eggs to stand mixer bowl. Beat on medium speed with the paddle attachment until light and fluffy.
Add vanilla bean paste and fresh lemon zest to sugar mixture. Beat on low speed until fully incorporated, about 30 seconds. Remove the bowl from the stand mixer. Set aside.
Add all-purpose flour, baking powder, and fine sea salt to small bowl. Whisk to combine.
Add half the flour mixture to the sugar mixture. Fold in with a large spatula. Add half the heavy cream to the cake batter. Fold in using a large spatula. Repeat the process with remaining flour and heavy cream.
Fold in the melted butter until the batter is smooth.
Transfer the cake batter to the prepared baking pan. Sprinkle reserved crumb topping over cake batter.
Bake in preheated oven for 45 minutes, or until a toothpick inserted in the center comes out clean.
Remove cake from oven and cool on wire rack. Run a paring knife around the edges of the cake and carefully invert to remove.
Dust with powdered sugar before serving.