In a mixing bowl, combine butter and brown sugar. Mix on high speed for at least 3 minutes with an electric mixer to "cream" them together and begin dissolving the sugar.
1 cup salted butter, 1½ cups light brown sugar
Add in the egg and vanilla extract and mix for 1 minute, until the egg is fully mixed in and the mixture is fluffy.
1 large egg, 1 teaspoon vanilla extract
In a blender, pulse the graham crackers until they become a fine powder, or you can smash them in a gallon sized bag with a rolling pin, just be sure to make sure they get very well smashed into a fine powder like sand.
12 graham crackers (2 cups crumbs)
Add the graham cracker powder, flour, baking soda, and salt (cinnamon optional) to the cookie dough and mix on low speed until everything is mixed in, about 1 minute.
2 cups all purpose flour , 1 teaspoon baking soda, ½ teaspoon salt
Scoop the cookie dough onto prepared baking sheets with a large 3-4 Tablespoon cookie scoop. Smash the cookies slightly so they are about 2 inches.
Bake at 350 ℉ for 10-12 minutes, they will be starting to crack around the edges. Let cool completely before frosting.
For the frosting:
In a mixing bowl, combine the powdered sugar and lemon zest and mix well.
2½ cups powdered sugar, 2 teaspoons lemon zest
Add butter, cream cheese, cornstarch and vanilla and mix at medium/high speed with an electric mixer until fluffy, about 1 minute.
½ cup salted butter, 4 oz cream cheese, 2 Tablespoons cornstarch, 1 teaspoon vanilla extract
Once the cookies are completely cool, transfer the cream cheese frosting to a piping bag and pipe onto each cookie starting on the outside, frosting in a spiral to the center.
Make the lemony glaze by combining the powdered sugar, lemon juice, and vanilla in a small bowl and whisking until smooth.
1½ cups powdered sugar, 2 Tablespoons lemon juice , ½ teaspoon vanilla extract
Drizzle the glaze over the frosted cookies. Optional: place a small, thinly sliced lemon triangle and/or lemon zest on top of each cookie and sprinkle with graham cracker crumbs.
Notes
TIP: Weigh your ingredients! You will have consistent results when you weigh instead of using cup measurements, especially since different graham cracker brands can be different weights. Store refrigerated for up to 3 days. Best when brought to almost room temperature to serve. Raw cookie dough, baked cookies, and frosting may all be frozen for up to 3 months separately.