Make Fresh Strawberry Cupcakes: Preheat oven to 375°F. In a medium-sized bowl, mix together flour, baking powder, and salt. Set aside.
In a stand mixer with the paddle attachment, beat together butter and vegetable shortening until smooth, about 1 minute. Add sugar and beat for 3 minutes. Add eggs one at a time, waiting until the first is fully incorporated before adding the second. Beat until light and fluffy, about 2 minutes.
In a small bowl, use a fork to mash the strawberry pieces. Add buttermilk and vanilla to the strawberries and mix well.
Change the paddle attachment to the whisk attachment and add the strawberry mixture to the mixer. Whip for 3 minutes. Add dry ingredients and whip on low until well combined, about 2 minutes.
Change the paddle attachment to the whisk attachment and add the strawberry mixture to the mixer. Whip for 3 minutes. Add dry ingredients and whip on low until well combined, about 2 minutes.
Place 12 paper baking cups in a 12-cup standard-size muffin pan, and divide batter evenly among baking cups (filling about two-thirds full). Bake until a toothpick inserted into the center comes out clean, 18-20 minutes. Allow to cool completely before frosting, about 1 hour.
Make Strawberry Frosting: Place freeze-dried strawberries in a blender or food processor, and blend until the strawberries are broken down into a powder. Set aside.
In a mixer, beat together butter, shortening, and cream cheese until well combined, about 2 minutes. Add powdered sugar, and beat on low for 1 minute before increasing the speed to medium-high for another minute. Add corn syrup, vanilla, and salt, and beat on medium-high until very fluffy, about 4 minutes. Cover cooled cupcakes evenly with frosting.