Line baking sheets with parchment paper and preheat the oven to 350°F.
In the bowl of your mixer, cream together the butter and sugars for about 1–2 minutes until light and creamy. Add the oil, sour cream, eggs, vanilla, and almond extract, mixing for another minute until everything is well combined.
In a separate medium bowl, whisk together the flour, baking soda, cream of tartar, and salt. With your mixer on the lowest setting, slowly incorporate the dry ingredients into the wet mixture, stirring just until combined. Be careful not to overmix the dough.
Place about ¼ cup of granulated sugar into a shallow dish. Using a medium scoop, portion out balls of dough and place them on the prepared baking sheet.
Then, take the flat bottom of a glass—or my personal favorite, the bottom of a ⅛ cup measuring cup—lightly spray it with cooking spray, dip it in the sugar, and press firmly into the center of each dough ball. You’ll want the dough to spread slightly around the edges, but don’t press too far. I prefer my cookies a bit thicker, so about ½-inch thickness is just right for me. But you can press until ¼ inch thickness as well. From here, no need to respray the bottom—the grease from the cookies will naturally keep it from sticking.
Bake for about 8 minutes. Keep a close eye on them—you’ll know they’re ready when the tops no longer look wet, but be sure not to let the edges brown, as that will make the cookies dry. Let them cool on the baking sheet for about five minutes before transferring them to a wire rack.
While the cookies cool, prepare the signature frosting. In a mixing bowl, beat together the butter, sour cream, and vanilla until smooth. Add in two cups of powdered sugar, then slowly mix in 3–4 tablespoons of milk until you reach a spreadable consistency. Taste and adjust with a tiny pinch of salt if needed. For that classic Swig look, add a drop of red food coloring and whip the frosting on high for 30 seconds to a minute until fluffy and perfectly pink.
Notes
-To make these larger cookies like Swig use a 3 Tablespoon scoop instead and adjust bake time by 1 minute or so. -Be sure and use softened butter, not melted. -Can substitute vanilla extract for the almond if desired.