In a food processor, pulse the graham crackers until uniform crumbs form. Transfer to a bowl and add the butter. Stir together until all the crumbs are moistened and resembles wet sand.
Add 1 tablespoon of the graham crumbs to each cupcake well and press down using the back of a spoon or small glass to compress and tighten. Bake for 6 minutes. Remove from oven and set aside to cool.
In a large bowl, whisk together the flour, baking powder, and salt. Set aside.
Add the strawberries to a food processor and pulse until pureed. Transfer to a small bowl and stir in the milk and vanilla. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, cream together the butter and sugar on medium speed. Beat until light and fluffy. Scrape down the bowl, reduce the speed to medium-low and add the egg and white, one at a time.
Scrape down the bowl and reduce the speed to low. Add about a third of the flour mixture and beat just until a few streaks remain. Add half of the strawberry puree and beat to combine. Then, add another third of the flour and beat just until a few streaks remain. Add the last half of the strawberry puree and beat to combine. Finally, add the remaining flour and beat just until a few streaks remain.
Fill each cupcake well 2/3 full and bake for 15 to 17 minutes, until a toothpick inserted comes out clean.