Preheat the oven to 350ºF. Line a baking sheet with parchment paper or a Silpat.
In the bowl of a food processor, blend the graham crackers until they are finely crushed and are the consistency of flour. Transfer the crushed graham crackers to a large bowl then stir in the flour and baking powder.
In the bowl of a stand mixer fitted with the paddle attachment, cream together the butter with the brown sugar until light and fluffy, about 2 minutes. Add the egg and beat until well combined then add the graham cracker mixture and beat just until combined.
Using a small ice cream scoop or two spoons, scoop about 2-tablespoon mounds of the dough onto the cookie sheet, spacing the mounds about 2 inches apart. Press your thumb (or use the back of a spoon) into the top of each mound to form a small indentation.
Clean out the stand mixer bowl then add the cream cheese, egg yolk, pumpkin purée, sugar, vanilla extract, and pumpkin pie spice and beat until well combined. Transfer the mixture to a piping bag or sealable plastic bag then pipe about 1 1/2 teaspoons of the mixture into the center of each cookie. Bake the cookies for about 12 minutes or until the cheesecake is set.
Remove the cookies from the oven and let them cool for 5 minutes on the cookie sheet before transferring them to a cooling rack to cool completely. Top each cooled cookie with a dollop of whipped cream and serve immediately.