Preheat oven to 350 degrees and line a muffin pan with 12 cupcake liners.
After you've finely crushed your graham crackers into crumbs (I pulsed it in a food processor), using a spatula, mix it with the melted butter and sugar until all is moistened.
Drop a tablespoon of graham cracker crumbs into the muffin cups and using the bottom of a Tabasco jar, firmly pack and press the graham cracker crusts. I used a Tabasco jar because it was the perfect size.
Bake for 5 minutes, remove from oven, set aside, and maintain oven temperature.
In a medium bowl, combine cake flour, baking powder, baking soda, and salt. Set aside.
In a bowl of a stand mixer, beat the butter on low until it's softened. Then add the sugar and increase the speed to medium. Beat until light and fluffy, about 5 minutes. Then add 1 egg at a time, beating well after each addition.
Add the lime juice, lime zest, and food coloring. Beat until well combined. It'll look curdled but it's okay :)
Add the flour in 3 separate additions, alternating with the buttermilk in the beginning and then ending with the flour mixture. Mix until well combined after each addition.
Fill the prepared cupcake liners with the batter, about 2/3 full.
Bake for 20-25 minutes and let cool completely before frosting.
While cupcakes are cooling, prepare the frosting by beating the butter and lime zest together for 3 minutes then add in the vanilla extract and salt. Combine well and slowly add in the powdered sugar, lime juice and lime zest. Spoon the frosting into a piping bag and pipe onto cooled cupcakes with whatever tip you prefer.
Keep in an airtight container, in the fridge, for about a week.
Notes
If you are in a pinch and can't wait for the eggs or buttermilk to come to room temperature, drop the eggs and bottle of buttermilk in a large bowl with warm water and have them sit in there for 10-15 minutes :)Cupcake recipe adapted from Bon Appetit, September 2008, frosting recipe barely adapted from All Recipes