BUTTER AND SUGARS: Melt the butter in a microwave-safe bowl in the microwave. Set aside and let cool to room temperature, about 5 minutes. (If the butter is hot when it is added to the sugars, it will melt the sugars and cause greasy cookies.) Once the butter has cooled, pour it into a large bowl. Add in the brown and white sugar. Stir well until completely incorporated and smooth.
EGGS AND VANILLA: Add in 1 full egg and then 1 egg yolk (discard the white or save for another recipe). Add in the vanilla and stir until smooth.
DRY INGREDIENTS: In another bowl, toss together the flour, baking soda, and salt. Add whole graham crackers to a blender or food processor and crush until you have 1 cup of very fine crumbs (gently pack in the measuring cup). Add the graham cracker crumbs to the dry ingredients. Stir everything to combine.
COMBINE: Combine the wet and dry ingredients and mix until just combined avoiding over-mixing.
ROLL COOKIE DOUGH BALLS: Using a tablespoon measuring spoon, get 2 tablespoons of dough per cookie (45g if you have a food scale per cookie). Roll the cookie dough balls large and tall (rather than round). Place on a parchment paper-lined plate, cover tightly and chill for 1 hour and up to 4 hours.
BAKE: Preheat the oven to 325 degrees F (162 degrees C) and line a pan with parchment paper or a Silpat liner. Space 6 cookies per cookie sheet (because they spread a lot). Bake for 10-14 minutes or until slightly browned at the edges. Remove from the oven and immediately use the back of a spoon to press the edges of each cookie into the center. (See video or photos.) Work quickly-- the cookies firm up quickly. This will give each cookie a great crispy edge. Let stand on the tray for 4 more minutes then use a spatula to remove the cookie from the sheet pan to a cooling rack. Let cool completely before frosting.
FROSTING: Meanwhile, make the frosting. In a stand mixer fitted with the whisk attachment (or a large bowl and a hand mixer), beat the softened (not melted) cream cheese and butter until creamy for about 2 minutes at medium-high speed. Add the powdered sugar, salt, and vanilla. Beat until the frosting is soft and creamy. Avoid overbeating the mixture or you'll get whipped frosting. (If the frosting does happen to be too wet, add a bit more powdered sugar and if it is too dry, add a touch of milk or cream.)
FROST AND DECORATE: Transfer the frosting to a plastic bag and cut off the tip of the bag. Pipe in a swirl around each completely cooled cookie. If desired, crush a bit of graham cracker on top of the cookie and garnish the center of each cookie with a piece of graham cracker. Drizzle a little bit of warm honey on top of each cookie. This is optional; a little goes a long way. Enjoy!
Note 1: If you press a measuring cup into a bag of flour, you will pack in way too much flour; use a spoon to scoop it into a measuring cup and then level the top with the back of a table knife.