Preheat oven to 350° F. Grease the edges of three 8" x 2" round cake pans. Dust with flour and tap out the excess. Line the bottom of each pan with a circle of parchment paper.
Puree the strawberries in a food processor. Strain the puree through a fine mesh sieve placed over a bowl to remove the seeds. In an electric mixer fitted with the paddle attachment, combine butter and half of the sugar. Beat on low speed until well blended. Add the other half of the sugar and two tablespoons of strawberry puree, mixing until combined. Increase speed to medium and add additional puree, a tablespoon at a time, until desired color and flavor is reached (I used all of the puree). Add vanilla and beat on high for about 30 seconds to lighten the frosting.
Place one cake layer on a cake stand, plate or cake board. Spread and smooth 3/4 cup frosting, using a small offset spatula. Repeat with second cake layer. Place the third cake layer on top and frost the top and sides of the cake with the remaining strawberry frosting. Refrigerate for at least 30 minutes and serve.
*Nutritional information is an estimate. Please consult a doctor or nutritionist for the most accurate nutritional info.