1. Make the Key Lime Curd:

• Combine the granulated sugar, Key lime juice, egg, and egg yolk in a small saucepan over medium-low heat.
• Whisk until the sugar dissolves, about 1 minute.
• Whisking constantly, add the cold butter, a few pieces at a time, waiting until it melts before adding more.
• Continue whisking until the curd is thick and coats the back of a spoon, 3 to 4 minutes.
• Transfer the curd to a small bowl and refrigerate until chilled, about 1 hour.

2. Make the Cupcakes:

• Preheat the oven to 350°F (175°C).
• Line 24 muffin cups with paper liners.
• Prepare the cake mix according to the package directions for cupcakes.
• Bake and cool as directed on the box.

3. Make the Frosting:

• Beat the softened butter, softened cream cheese, and Key lime juice in a large bowl with a mixer on medium-high speed until light and fluffy, 3 to 4 minutes.
• Reduce the speed to low and slowly add the powdered sugar.
• Continue to beat until just combined, 1 to 2 minutes. Be careful not to overbeat.

4. Assemble the Cupcakes:

• Use a paring knife to cut a small hole in the top of each cooled cupcake, about 1/2 inch deep and 1/2 inch in diameter.
• Spoon 1/2 teaspoon of the chilled Key lime curd into each hole.
• Spread the frosting on the cupcakes.
• Sprinkle with graham cracker crumbs.
• Top each cupcake with a thin lime slice.