Preheat oven to 350°F (180°C). Lightly spray bottom of a 17½x12½- inch rimmed baking sheet with baking spray with flour. Line bottom of pan with parchment paper; lightly spray parchment.
In the heatproof bowl of a stand mixer, whisk together eggs, granulated sugar, and vanilla bean paste by hand. Place bowl over a saucepan of simmering water. Cook, whisking constantly, until an instant-read thermometer registers 110°F (43°C).
Carefully return bowl to stand mixer. Using the whisk attachment, beat at high speed until thick, tripled in volume, and ribbon-consistency, 3 to 4 minutes.
In a medium bowl, sift together flour, baking powder, and salt. Using a large balloon whisk, gently fold flour mixture into egg mixture in two additions just until combined.
In a small bowl, whisk together sour cream and oil.
Transfer 1 cup (112 grams) batter to another small bowl, and whisk in sour cream mixture until combined. Fold sour cream mixture into batter in two additions just until combined. Pour batter into prepared pan, and smooth flat with an offset spatula using as few strokes as possible.
Bake until set and top springs back when gently touched, 11 to 13 minutes. Let cool completely in pan on a wire rack.
Run a knife along edges of pan to loosen cake, if needed. Using a serrated knife, cut cooled cake into 4 (12×4-inch) rectangles, being sure to cut through the parchment paper as well; use scissors if needed. (You will have some leftover cake; reserve for another use if desired.)
Gently brush each rectangle with Vanilla Simple Syrup. (You will have leftover syrup.) Lift each piece, with parchment attached, out of pan. Spread 2 tablespoons (40 grams) preserves on each rectangle; spread ½ cup (63 grams) Whipped Cream Cheese Filling onto each rectangle.
Gently brush each rectangle with Vanilla Simple Syrup. (You will have leftover syrup.) Lift each piece, with parchment attached, out of pan. Spread 2 tablespoons (40 grams) preserves on each rectangle; spread ½ cup (63 grams) Whipped Cream Cheese Filling onto each rectangle.
Starting with one short side, roll up 1 rectangle into a log, removing parchment as you roll, and place in center of a cake plate. (Don’t roll too tightly or the cake will crack.) Carefully wrap a second rectangle around center roll, using parchment to help. Repeat with remaining cake rectangles, creating a spiral.
Spoon 1 cup (126 grams) Whipped Cream Cheese Filling into a pastry bag fitted with a medium open star piping tip (Ateco #825). Spread remaining whipped filling on top and sides of cake. Spoon remaining preserves on top of cake, leaving about a ½-inch border around edges. Pipe whipped filling along edges. Refrigerate cake for at least 2 hours before serving. Refrigerate in an airtight container for up to 3 days.