Adjust oven racks to the middle positions. Preheat oven to 350 degrees F. Line muffin tins with paper liners; set aside.
In a medium bowl add flour, cornstarch, baking powder, and salt. Use a whisk to mix until combined; set aside.
In the bowl of a stand mixer fitted with a paddle attachment (or in a large bowl with a handheld mixer), cream the butter and sugar together on medium speed for 2-4 minutes, or until light, fluffy, and pale in color. Add the eggs and vanilla, and pulse until just combined.
Add one third of the dry ingredients, give a few pulses to mix until combined and no lumps remain. Do the same with 1/3 of the milk. Scrape down the sides of the bowl and repeat, alternating between the dry ingredients and milk. Once everything is combined, add the pureed strawberries and fold into the batter until combined and no streaks remain.
Scoop batter into prepared muffin tins using a 3-tablespoon scoop, filling the muffin cups two-thirds full. Bake for 16-18 minutes, or until a toothpick comes out clean. Rotate muffin tins halfway through baking.
Cool the cupcakes in the muffin tins for 10 minutes, then remove them from the tins to a wire rack to cool completely before frosting.
FOR THE STRAWBERRY CREAM CHEESE FROSTING:
Add the pureed strawberries to a small saucepan over medium-low heat. Simmer, stirring occasionally until reduced to about 3 tablespoons. This will take about 10 - 14 minutes. Pour mixture into a small bowl and chill until cool, about 15-20 minutes.
Once the pureed strawberries are cool, beat the butter and cream cheese on medium speed until creamy and blended. This will take about 2 minutes. Add the vanilla and pureed strawberries and beat on medium speed until combined, about 30 seconds. Add the confectioner’s sugar and pulse until combined, increase speed to medium and beat until light and creamy, about 2 minutes.
Transfer frosting to a piping bag fitted with a decorating tip (I used Wilton’s 1M tip). Pipe onto cupcakes. Finish with sliced strawberries (optional), and serve immediately or cover and chill until ready to serve.