Remove the stems from 1½ packages of the strawberries and pulse in a food processor or blender until pureed. Set aside the remaining strawberries for garnish.
Pour the strawberry puree into a medium saucepan and cook over medium heat for about 20 minutes, or until the mixture is reduced to ¾ cup. (The mixture will look like tomato paste.) Set aside to cool completely.
Preheat the oven to 350°F. Grease 2 (9-inch) pans with vegetable shortening and line the bottoms with parchment paper.
Beat the butter and sugar at medium speed with a heavy-duty stand mixer until light and fluffy. Add the mayonnaise and beat until creamy. Add the eggs, one at a time, beating well after each addition. Beat in the vanilla.
Stir together the flour, baking powder, and baking soda in a medium bowl. Add the flour mixture to the butter mixture alternately with the milk in three additions, beginning and ending with the flour. Beat in the cooled strawberry puree and add a few drops of red food coloring, if desired.
Divide the batter evenly between the prepared cake pans. Tap the pans on the counter to remove any air bubbles. Bake in the preheated oven for 28 to 32 minutes or until a toothpick inserted in the center comes out clean.
Remove the cakes from the oven and let cool for 5 minutes. Run a knife around the edges of the pans and turn out onto wire racks to cool completely.
While the cakes bake and cool, make the strawberry frosting: Process the freeze-dried strawberries in a food processor until they form a powder.
Beat the butter at medium speed with an electric mixer until creamy. Add the strawberry powder, milk, and vanilla, and beat until combined. Add the powdered sugar, 1 cup at a time, and beat until smooth and spreadable.
To assemble the cake, trim the cake layers to make them level, if desired. Place one cake layer on a cake stand or plate. Pipe a thin ring of buttercream around the edge.
Top with the preserves, and spread to the piped edges of frosting.
Place the second cake on top of the first. Frost the top and sides of the cake with the remaining buttercream. Decorate the top with the reserved strawberries and garnish with mint, if desired.