• Preheat the oven to 350 degrees Fahrenheit. Line 2 baking sheets with parchment paper and set them aside.
• In a medium bowl, whisk together 5 ½ cups all-purpose flour, ½ teaspoon baking soda, ½ teaspoon cream of tartar, and 1 teaspoon salt. Set aside.
• In a large bowl, beat 1 cup softened unsalted butter, ¾ cup vegetable oil, 1 ¼ cups granulated sugar, ¾ cup powdered sugar, and 2 tablespoons water togther on medium-high speed with a hand mixer or stand mixer fitted with the paddle attachment for 2-3 minutes, until light and creamy. Add 1 teaspoon lemon juice, 1 tablespoon lemon zest, and 2 large eggs,.
• Slowly mix the flour mixture into the sugar mixture just until combined. Scoop the dough into ¼ cup portions and roll them into uniform balls. Place the cookie dough balls on the parchment-lined baking sheets, leaving 2-inches between the cookies.
• To give the cookies their signature rough edge, dip the bottom of a flat-bottomed glass into ¼ cup granulated sugar, and press the glass onto the cookie dough ball to flatten the cookie to about ½-inch thickness.
• Bake for 8-10 minutes or until the edges are set and the bottom is very lightly browned. These cookies should be quite soft, so please be careful not to overbake them. Let them cool on the baking sheet for 2 minutes before transferring to a cooling rack to cool completely.

Lemon Cream Cheese Frosting

• In a large bow, beat 4 ounces softened cream cheese, 2 tablespoons salted butter, 1 tablespoon lemon juice, 1 teaspoon lemon zest, and ½ teaspoon vanilla extract together until smooth and creamy. Add 2 ½ cups powdered sugar and beat until combined and creamy.
• Frost the cooled cookies generously before serving.