Preheat oven to 350 degrees F. Line a 12-cup standard muffin tin with paper liners; set aside.
In a large bowl, combine flour, cornstarch, baking powder and salt.
In the bowl of an electric mixer fitted with paddle attachment, beat sugar, eggs and vanilla on medium speed until light and fluffy, about 2-3 minutes. Beat in vegetable oil and butter until well combined. With mixer on low speed, add dry ingredients and milk alternately in 3 parts, beginning and ending with dry ingredients, beating just until incorporated. Add strawberries and gently toss to combine.
Scoop the batter evenly into the muffin tray. Place into oven and bake for 15-18 minutes, or until a tester inserted in center comes out clean. Remove from oven and cool completely on a wire rack before frosting.
In the bowl of a food processor, combine freeze dried strawberries until finely ground, about 1-2 minutes; set aside.
In the bowl of an electric mixer fitted with the paddle attachment, beat butter and 3 1/2 tablespoons strawberry powder on medium speed until light and fluffy approximately 1-2 minutes. With the mixer on low speed, gradually add heavy cream and confectioners’ sugar, beating just until incorporated. Increase speed to medium high and beat until frosting is light and fluffy, approximately 1-2 minutes.
Use a small offset spatula or a pastry bag fitted with a decorative tip to frost cupcakes, garnished with strawberry half, if desired.