Preheat oven to 350°F (180°C). Line a 13×9-inch baking pan with parchment paper, letting excess extend over sides of pan; lightly brush only bottom of parchment paper with baking spray with flour.
In the heatproof bowl of a stand mixer, whisk together eggs and sugar 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; add extracts. 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 a small bowl, and whisk in sour cream mixture until combined. Fold sour cream mixture into batter in two additions just until combined. Spread batter into prepared pan with an offset spatula, using as few strokes as possible.
Bake until top springs back when gently touched and a wooden pick inserted in center comes out clean, about 30 minutes. Let cool completely in pan on a wire rack.
Run a knife around edges of pan to loosen cake. Using excess parchment as handles, remove cake from pan, and transfer to a large cutting board. Using a long serrated knife, cut cake in half horizontally. Using a cake lifter or cake board, gently separate layers.
Using a cake lifter or cake board, return bottom half of cake, cut side up, to baking pan. Using a pastry brush, generously brush Almond Simple Syrup onto cake. Spread Pastry Cream onto cake. Top with strawberries, gently pressing into cream.
Place top half of cake, cut side down, on strawberries. Generously brush with Almond Simple Syrup. Cover with plastic wrap, and refrigerate for at least 4 hours or up to overnight.
Just before serving, spread Roasted Strawberry Mascarpone Whipped Cream onto cake. Garnish with candied almonds, if desired. Cover and refrigerate for up to 3 days.