Adjust oven rack to middle position and heat oven to 350 degrees F. Line your muffin tin with baking papers. Grind graham crackers, flour, baking powder, and salt in food processor to fine crumbs (5 5-second pulses should do the trick). Whisk milk and vanilla in measuring cup.
With electric mixer on medium-high speed, beat sugar, butter, and shortening until light fluffy, about 2 minutes. Beat in eggs, one at a time, until combined. Beat on medium-high speed until mixture is lighter in color and somewhat fluffy, about 2 minutes. Reduce speed to low and add graham cracker mixture in 3 additions, alternating with 2 additions of milk mixture, until incorporated.
Fill each well of the muffin tin 3/4 of the way full. Bake until toothpick inserted in center comes out clean, 15-18 minutes. Cool in muffin tin for 10 minutes, then transfer cupcakes to wire rack to cool completely, about 20 minutes.
For the Milk Chocolate Frosting:
Using a handheld or stand mixer fitted with a paddle attachment, beat the butter on high speed until smooth and creamy - about 2 minutes. Add the confectioners' sugar, cocoa powder, and salt. Pulse on lowest setting until the sugar and cocoa are absorbed into the butter, about 2 minutes. Turn mixer to medium speed and add the vanilla and milk. Once incorporated, turn the mixer to high speed and beat for 1 minute. If you'd like a thicker frosting, add more confectioners' sugar, 2 tablespoons at a time, until your desired thickness is reached.
Pipe or spread the frosting onto cooled cupcakes. Garnish with the marshmallows.