Make strawberry puree: Place strawberries in a food processor or blender; process until smooth, about 30 seconds, stopping to scrape down sides of bowl as needed; set aside.

Prepare oven and cake pans: Preheat oven to 350°F with rack in center position. Coat 2 (9-inch) round cake pans with baking spray. Line bottoms with parchment paper, and lightly coat parchment with baking spray; set aside.

Combine dry ingredients: Whisk together flour, baking powder, and 1 teaspoon of the salt in a medium bowl.

Mix butter, sugar, and gelatin: Beat granulated sugar, gelatin, and 1 cup of the butter in a stand mixer fitted with a paddle attachment on medium speed until light and fluffy, stopping to scrape down sides of bowl as needed, about 3 minutes.

Add eggs and vanilla: With mixer on low, beat in eggs, one at a time, beating well after each addition. Beat in ½ teaspoon of the vanilla until just combined.

Finish cake batter: Whisk together milk and ½ cup of the reserved strawberry puree in a 2-cup measuring cup. With mixer on low, alternately add flour mixture and milk mixture, beginning and ending with flour mixture, beating until just combined after each addition, about 2 minutes total.

Add batter to pans: Divide cake batter evenly among prepared pans, spreading batter into an even layer.

Bake cake layers: Bake in preheated oven until a wooden pick inserted in centers comes out clean, 25 to 28 minutes. Let cakes cool in pans 15 minutes. Remove cakes from pans, and discard parchment paper. Let cool completely on wire racks, about 1 hour.

Make strawberry reduction: Meanwhile, place remaining ¾ cup strawberry puree in a small saucepan; bring to a simmer over medium, stirring occasionally. Reduce heat to medium-low; cook, stirring occasionally, until reduced to ¼ cup, about 15 minutes. Remove from heat, and transfer to a small bowl; refrigerate, uncovered, until completely cooled, about 30 minutes.

Cream butter for frosting: Once cakes have cooled, beat together remaining 1 cup butter, ¼ teaspoon salt, and ¼ teaspoon vanilla in a stand mixer fitted with a paddle attachment on medium speed until smooth and fluffy, about 3 minutes.

Add sugar and reduction to butter: With mixer on low, alternately add powdered sugar and cooled strawberry reduction, beating until just combined after each addition. Increase speed to medium, and beat until fluffy, about 1 minute.

Assemble cake: Place 1 cooled cake layer on a serving plate or cake stand. Spread about 1 cup of the frosting in an even layer over top of cake layer.

Garnish and serve: Top with remaining cooled cake layer. Spread remaining 2 cups frosting evenly over top and sides of cake; swoop or smooth as desired. Garnish with additional fresh strawberries.