Preheat oven to 350°F (175°C). Line a large baking sheet with parchment paper or a silicone baking mat.

In a large bowl, whisk together 2 3/4 cups all-purpose flour, 1/2 teaspoon baking soda, 1/2 teaspoon cream of tartar, and 1/2 teaspoon kosher salt. Set the dry mixture aside.

In a separate large bowl, use an electric mixer to beat 1/2 cup (1 stick) unsalted butter (room temperature), 1/2 cup vegetable or canola oil, 1/2 cup of the granulated white sugar, and 1/2 cup powdered sugar until smooth and combined.

Add 1 large egg, 1 teaspoon vanilla extract, and 1/2 teaspoon almond extract to the butter mixture. Mix until incorporated.

With the mixer on low speed, add the dry ingredient mixture to the wet ingredients and mix just until the dough comes together. Do not overmix.

Scoop or roll the dough into about 24 balls (about 2 tablespoons of dough per cookie). Place the dough balls on the prepared baking sheet about 2 inches apart. (Not all cookies will fit on the sheet at once—bake in batches.)

Pour the remaining 1/4 cup granulated white sugar onto a small plate. Spray the bottom of a drinking glass lightly with nonstick cooking spray and press the glass bottom into the sugar so it is coated.

Press the sugared glass bottom gently onto the top of each dough ball to flatten to a cookie shape. Re-coat the glass with sugar as needed between cookies to prevent sticking and to keep an even sugared top.

Bake cookies in the preheated 350°F oven for 8 minutes. Do not overbake: cookies will still look light in color and soft in the center—this is correct.

Remove the baking sheet from the oven and let the cookies cool on the sheet for 5 minutes. Transfer the cookies to a wire cooling rack to cool completely. Allow the baking sheet to cool completely before reusing for the next batch.

For the frosting: in a large bowl, use a mixer to beat 3/4 cup (1 1/2 sticks) unsalted butter (room temperature) until smooth. Add 3 cups sifted powdered sugar and mix until combined.

With the mixer running, stream in 3 tablespoons heavy cream or milk, 1 1/2 teaspoons pure vanilla extract, and 3/4 teaspoon almond extract. Beat until the frosting is smooth. If the frosting is too thick, add a little more cream; if it is too thin, add a little more powdered sugar.

Use a butter knife to spread the frosting over the tops of the cooled cookies. Decorate with sprinkles, if desired.

Store frosted cookies in an airtight container at room temperature for up to 3 days.