Strawberry Shortcake with Thyme and Whipped Cream

Place a rack in middle of oven; preheat to 350°F. Line bottom of pans with parchment paper, leaving sides unlined and ungreased. Melt butter in a small pot over medium heat; set aside.
Whisk eggs, sugar, and salt in the bowl of a stand mixer. Place stand mixer bowl over a pot of barely simmering water and cook, whisking constantly, until mixture is warm to the touch and sugar is dissolved (use your fingers to check). Transfer bowl to stand mixer and beat on medium-high speed with the whisk attachment until mixture is cooled and tripled in volume, about 5 minutes (when you lift the whisk, mixture should fall back on itself in thick ribbons).
Transfer melted butter to a medium bowl. Add thyme, vanilla, and 1 cup egg mixture to butter and whisk to combine.
Transfer remaining egg mixture to a large wide bowl. Sift half of the flour over egg mixture. Using a rubber spatula or large balloon whisk, fold flour gently into egg mixture until almost fully incorporated. Repeat with the remaining flour, then fold in butter mixture with spatula just until incorporated. Gently divide batter between prepared pans; smooth surface.
Bake cakes until tops are deep golden and centers spring back when pressed lightly, 25–30 minutes. Immediately run a knife around edges and remove springform. Transfer pans to a wire rack and let cakes cool completely.
Bring sugar, thyme, and 1/2 cup water to a boil in a small saucepan. Let sit until cool, about 30 minutes. Strain through a fine-mesh sieve into a measuring cup and chill until ready to use.
Using a serrated knife, trim top of each cake to make them flat. Brush tops with 2–3 Tbsp. syrup per cake, depending on how concentrated you'd like the thyme flavor to be.
Toss 10 oz. strawberries with1 Tbsp. syrup in a medium bowl and let sit at least 10 minutes or up to 1 hour.
Meanwhile, whip heavy cream to soft peaks in the bowl of stand mixer fitted with the whisk attachment. Add sour cream and 2 Tbsp. syrup and whip to stiff peaks.
Transfer 1 cake layer to a platter and top with syrup-macerated strawberries. Top with half of the whipped cream, then place second cake layer gently on the first. Top with remaining whipped cream. Chill to set, at least 1 hour. Just before serving, arrange remaining 6 oz. strawberries, baby strawberries, if using, and thyme over cake.
Cakes can be baked and syrup-soaked, but not assembled, 2 days ahead; wrap layers separately in plastic and chill. Thyme syrup can be made 5 days ahead; chill in a resealable container. Assembled cake can be made 12 hours ahead; chill.