To make syrup, combine rosé and sugar in a medium saucepan over medium-high heat. Bring to a boil; reduce heat and simmer 15 to 20 minutes or until mixture is syrupy and reduced by about 1/
To make cake layers, combine strawberries and rose in a small bowl; let stand 30 minutes. Transfer mixture to a blender; process until smooth.
Preheat oven to 350°. Spray 3 (9-inch) round baking pans with baking spray; line bottom of each pan with parchment paper rounds. Spray parchment paper with baking spray; lightly flour each pan.
Combine strawberry puree, milk, egg whites, egg yolks, and vanilla in a medium bowl, stirring with a whisk until combined; set aside. Combine flour, baking powder, and salt in a medium bowl, stirring with a whisk; set aside. Combine sugar and butter in the bowl of a stand mixer fitted with a paddle attachment; mix at medium speed until pale and fluffy.
Add 1/2 of flour mixture to sugar mixture in bowl; mix at medium-low speed until combined. Add all of strawberry liquid mixture to bowl; mix at medium-low speed until combined. Add remaining flour mixture to bowl; mix at medium-low speed until just combined. Divide batter evenly between 3 prepared pans, smoothing tops with a rubber spatula. Bake at 350° in center of oven for 25 minutes or until skewer inserted in center of cake comes out clean, rotating pans halfway through baking.
Let cakes stand in pans 5 minutes. Run a butter knife around the edge of pans to loosen; invert cakes onto parchment paper-lined wire racks. Prick surface of cake layers all over with a wooden skewer; brush layers evenly with about 3/4 cup rose syrup. Let cakes cool completely.
To make frosting, combine powdered sugar, butter, and salt in a stand mixer fitted with a whisk attachment; mix at medium-low speed until combined. Increase speed and beat until fluffy. With mixer running, slowly stream in 1/3 cup rosé syrup; mix until combined. Add 1 Tbsp. rosé, mixing until combined.
To assemble cake and garnish, combine strawberries, rosé, and sugar in a medium bowl; let stand 20 to 30 minutes. Trim cooled cake layers. Stack cake layers, spreading frosting evenly between layers. Frost top and sides of cake, if desired. Gently spoon strawberries on top of cake. Slice as desired.