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Special equipment: a piping bag fitted with a tip
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For the graham cracker crust: Preheat the oven to 350 degrees F. Line a standard muffin pan or cupcake pan with 12 cupcake liners.
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In a small mixing bowl, combine the graham cracker crumbs, butter, granulated sugar and salt and mix well with a fork.
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Drop about 1 tablespoon of the graham cracker mixture into the bottom of each cupcake liner and press down to line the bottom.
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Bake for 5 minutes.
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Remove from the oven but keep the oven on.
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For the cake batter: In a saucepan, melt the butter over medium-low heat.
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Continue to cook, swirling occasionally, until the butter turns golden brown and there are little burnt bits at the bottom of the pan.
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Skim the foam from the top and pour it into a bowl (including the brown bits) to stop the cooking.
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Let cool to room temperature.
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In a medium bowl, sift together the flour, baking powder, cinnamon, baking soda and salt and set aside.
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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.
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Beat in the eggs and then scrape down the bowl.
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Mix in the sweet potato puree and vanilla extract, beating until just combined.
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Reduce the mixer speed to low and add in the dry ingredients, mixing until just incorporated.
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Divide the batter among the cupcake liners with the graham cracker crust, filling them three-quarters full.
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Bake until a tester inserted into the centers comes out clean, about 20 minutes.
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Set the pan on a rack to cool.
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For the frosting: In a large mixing bowl, beat the cream cheese, butter, maple syrup and maple extract together until smooth.
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Add the confectioner' sugar and beat on low speed until incorporated.
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Increase the speed to high and mix until very light and fluffy.
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Add the salt and mix to incorporate.
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To assemble: Use a piping bag to frost the cooled cupcakes generously.
