For the graham cracker crust: Preheat the oven to 350 degrees F. Line a standard muffin pan or cupcake pan with 12 cupcake liners.
In a small mixing bowl, combine the graham cracker crumbs, butter, granulated sugar and salt and mix well with a fork.
Drop about 1 tablespoon of the graham cracker mixture into the bottom of each cupcake liner and press down to line the bottom. Bake for 5 minutes. Remove from the oven but keep the oven on.
For the cake batter: In a saucepan, melt the butter over medium-low heat. Continue to cook, swirling occasionally, until the butter turns golden brown and there are little burnt bits at the bottom of the pan. Skim the foam from the top and pour it into a bowl (including the brown bits) to stop the cooking. Let cool to room temperature.
In a medium bowl, sift together the flour, baking powder, cinnamon, baking soda and salt and set aside.
In the bowl of a stand mixer with a paddle attachment, cream together the brown sugar and browned butter on medium-high speed until light and fluffy. Beat in the eggs and then scrape down the bowl. Mix in the sweet potato puree and vanilla extract, beating until just combined. Reduce the mixer speed to low and add in the dry ingredients, mixing until just incorporated.
Divide the batter among the cupcake liners with the graham cracker crust, filling them three-quarters full. Bake until a tester inserted into the centers comes out clean, about 20 minutes. Set the pan on a rack to cool.
For the frosting: In a large mixing bowl, beat the cream cheese, butter, maple syrup and maple extract together until smooth. Add the confectioner' sugar and beat on low speed until incorporated. Increase the speed to high and mix until very light and fluffy. Add the salt and mix to incorporate.
To assemble: Use a piping bag to frost the cooled cupcakes generously.
This recipe was created by a contestant during a cooking competition. It has not been tested for home use.