Aperol Spritz Cake with Prosecco-Poached Rhubarb

Preheat oven to 350°F. Grease a 9-inch round cake pan with oil, and line bottom of pan with parchment paper. Lightly grease parchment with oil. Set aside.

Whisk together eggs and 3/4 cup sugar in a large bowl until pale and foamy, 1 to 2 minutes. Whisk in 11/4 cups Prosecco, butter, and oil until well combined. Add flour, baking powder, 3/4 teaspoon salt, and baking soda; whisk until combined and almost smooth. Pour batter into prepared cake pan, and tap pan on counter to release any trapped bubbles.

Bake in preheated oven until a wooden pick inserted in center of cake comes out clean, 22 to 26 minutes. Transfer cake pan to a wire rack, and let cool 15 minutes. Run a small offset spatula around edge of pan, and invert cake onto a wire rack. Let cool completely, about 30 minutes.

Meanwhile, stir together Aperol, remaining 1 cup sugar, remaining Prosecco (about 2 cups), and remaining 1/4 teaspoon salt in a large saucepan. Bring to a simmer over medium-high, stirring occasionally to dissolve sugar. Add rhubarb to mixture, and fan orange slices over surface to keep rhubarb submerged in liquid. Return mixture to a simmer over medium-high. Reduce heat to medium-low to keep poaching liquid just below a simmer, and cook, gently swirling pan occasionally, until rhubarb is very tender but still holds its shape, 6 to 10 minutes. Remove from heat. Remove orange slices, and spread on a plate; let stand until cool enough to handle, about 5 minutes. Using a slotted spoon, carefully transfer delicate poached rhubarb to a fine wire-mesh strainer set over a medium bowl; set aside.

Bring poaching liquid in saucepan to a boil over high. Squeeze cooled orange slices over poaching liquid in pan; discard squeezed orange slices. Boil mixture, stirring occasionally, until liquid thickens to a syrupy consistency, coats the back of a spoon, and reduces to about 3/4 cup, 20 to 24 minutes. Remove from heat. Pour into a large heatproof bowl, and let cool to room temperature, about 1 hour.

When ready to serve, transfer cake to a rimmed plate or a cake stand. Add drained rhubarb to cooled syrup in saucepan, and toss to coat. Spoon rhubarb mixture over top of cake, piling rhubarb pieces in center. Let syrup soak into cake 10 minutes. Slice and serve.