Lightly spray a 9x13-inch pan with cooking spray and preheat oven to 350 degrees.
Place 2 cups of strawberries in a blender or food processor and process until very finely chopped. Measure out 1 cup.
Add cake mix, eggs, and vegetable oil to a mixing bowl. Use a hand mixer or stand mixer to mix well.
Mix in the 1 cup of strawberry puree and the (dry) strawberry gelatin.
Pour batter into prepared pan and bake for 30 to 35 minutes or until a wooden pick inserted in the center comes out clean. Let cool.
Make frosting. Process the remaining 2 cups strawberries in a blender or food processor until smooth. If you had leftover strawberries from making the cake batter, you can combine them.
Place strawberry puree in a small saucepan and bring to a simmer. Cook, stirring occasionally until thickened. You should have about 1/3 a cup. Let cool completely.
Use an electric mixer to beat butter until creamy.
Beat in 1 cup of sugar and then half of the 1/3 cup of reduced strawberry puree.
Beat in vanilla extract.
Beat in another cup of confectioners' sugar and remaining puree.
Beat in final cup of confectioners' sugar. Spread frosting on cooled cake.