The Best Swig Sugar Cookies

Ingredients

• 1 cup (227 g) salted butter, softened
• ¾ cup neutral-flavored oil, canola, vegetable, grapeseed, etc
• 1 ¼ cups (265 g) granulated sugar
• ¾ cup (86 g) powdered sugar
• ½ teaspoon baking soda
• ½ teaspoon cream of tartar or baking powder
• ½ teaspoon salt
• 2 tablespoons sour cream
• 2 large eggs
• 1 teaspoon vanilla extract (see note)
• 5 ½ cups (781 g) all-purpose flour (I use unbleached)
• Granulated sugar for pressing the cookies
• ¾ cup (170 g) salted butter, softened
• 1 teaspoon vanilla extract
• 6 cups (684 g) powdered sugar
• 1-2 tablespoons cream or milk