Melt the butter in a microwave-safe bowl. Set aside and let cool to room temperature, about 5 minutes. Once cooled, pour into a large bowl. Add the brown and granulated sugar and stir well until completely incorporated and smooth.

Add 1 whole egg and 1 egg yolk. Add vanilla extract and stir until smooth.

In another bowl, whisk together the flour, baking soda, and salt. Crush whole graham crackers until you have 1 cup of fine crumbs and add them to the dry ingredients. Stir to combine.

Combine the wet and dry ingredients and mix until just combined, avoiding overmixing.

Using a tablespoon, scoop 2 tablespoons of dough per cookie. Roll into balls and place on a parchment-paper-lined plate. Cover tightly and chill for at least 1 hour.

Preheat oven to 325°F (162°C). Line a baking sheet with parchment paper. Space 6 cookies per sheet and bake for 10–14 minutes, or until slightly browned at the edges. Immediately press the edges of each cookie inward with the back of a spoon. Let stand on the tray for 4 more minutes, then transfer to a cooling rack. Let cool completely.

In a stand mixer or with a hand mixer, beat the softened cream cheese and butter until creamy, about 2 minutes. Add the powdered sugar, salt, and vanilla extract. Beat until the frosting is soft and creamy.

Transfer the frosting to a piping bag and pipe a swirl onto each cooled cookie. Optionally, garnish with crushed graham crackers, a piece of graham cracker, and a drizzle of honey.