Instructions

• Melt 12 tablespoons (3/4 cup) unsalted butter in a microwave-safe bowl. Let the butter cool to room temperature, about 5 minutes (hot butter will melt the sugars and make greasy cookies).
• In a large bowl, add the cooled melted butter, 1/2 cup granulated sugar, and 3/4 cup light brown sugar (lightly packed). Stir until the sugars are fully incorporated and the mixture is smooth.
• Add 1 large egg, 1 large egg yolk (discard or save the white), and 1/2 tablespoon vanilla extract to the butter-sugar mixture. Stir until smooth and combined.
• In a separate bowl, whisk together 1-3/4 cups all-purpose flour, 1 teaspoon baking soda, and 1/2 teaspoon salt.
• Place whole graham crackers in a blender or food processor and pulse until you have 1 cup of very fine graham cracker crumbs (gently packed), about 9 full sheets. Add the graham cracker crumbs to the bowl with the dry ingredients and stir to combine.
• Add the dry ingredient mixture to the wet ingredients and mix just until combined. Do not overmix.
• Using a tablespoon measure, portion 2 tablespoons of dough per cookie (about 45 g if you use a scale). Form each portion into a tall mound rather than a smooth round ball. Place the dough mounds on a parchment-lined plate or baking sheet, leaving space between them. Cover tightly and chill in the refrigerator for 1 hour (up to 4 hours).
• When ready to bake, preheat the oven to 325°F (162°C). Line a baking sheet with parchment paper or a silicone liner. Place no more than six chilled dough mounds on one sheet (cookies spread).
• Bake for 10–14 minutes, until the cookie edges are slightly browned. Remove the tray from the oven.
• Immediately and quickly press the edges of each cookie toward the center using the back of a spoon to form a crisp edge (the cookies firm up quickly). Let the cookies stand on the baking sheet for 4 minutes, then transfer them to a wire rack to cool completely.
• While the cookies cool, make the frosting: in a stand mixer fitted with the whisk attachment (or a large bowl and hand mixer), beat 4 ounces block cream cheese (softened, not melted) and 4 tablespoons unsalted butter (softened, not melted) at medium-high speed until creamy, about 2 minutes. Add 2 cups powdered sugar, 1/8 teaspoon salt, and 1 teaspoon vanilla extract. Beat until the frosting is soft and creamy, taking care not to overbeat (overbeating will make whipped frosting). If the frosting is too wet, add a little more powdered sugar; if it is too firm, let it sit at room temperature a few minutes and beat briefly to loosen.
• Transfer the frosting to a plastic bag or piping bag, snip off the tip, and pipe a swirl of frosting onto each completely cooled cookie.
• Let the frosting set briefly if desired, then serve.