Preheat oven to 350°F (180°C). Spray 2 (17¼×12¼-inch) rimmed baking sheets with baking spray with flour. Line bottom of pans with parchment paper; spray parchment.

In the bowl of a stand mixer fitted with the whisk attachment, beat butter, sugar, vanilla bean paste, and salt at low speed, and slowly increase mixer speed to high. Beat until light and fluffy, 6 to 8 minutes, stopping to scrape sides of bowl after 3 minutes. Reduce mixer speed to medium, and add eggs, one at a time, beating until combined after each addition. With the mixer on low speed, slowly add flour, beating just until combined. Divide batter between prepared pans (about 804 grams each). Using an offset spatula, spread batter into an even layer.

Bake until edges are golden and a wooden pick inserted in center comes out clean, 10 to 12 minutes. Let cool completely in pans.

Brush cooled cakes with Vanilla Simple Syrup. Freeze until firm, about 30 minutes.

Remove 1 cake from pan; discard parchment. Trim sides of cake to make a 15×11-inch rectangle. Cut rectangle into 3 (11×5-inch) rectangles. Repeat with remaining cake.

Place 1 cake rectangle on a serving platter. Spread ¾ cup (188 grams) Chocolate Buttercream on top, smoothing into an even layer. Top with second rectangle, and spread ¾ cup (188 grams) buttercream on top, smoothing into an even layer. Repeat procedure three times. Top with remaining rectangle. Spread remaining Chocolate Buttercream on top and sides of cake. Refrigerate until buttercream is set, 30 to 45 minutes.

Spoon Caramel Sauce on top of cake, letting it slowly drip down sides.