Preheat your oven to 350 degrees and line two large baking sheets with parchment paper.

In a medium bowl, stir together the flour, salt, baking powder, and baking soda. Set this mixture aside. In a large bowl, beat together the butter, oil, sugar, and lemon zest until the mixture is well combined and lightened in color, about 2 minutes. Then beat in the egg, vanilla extract, and sour cream until well combined.

Slowly add in the dry ingredients, mixing until well combined. Using a large cookie scoop, scoop about 6 cookies per baking sheet, leaving room for the cookies to spread as they bake. You should use about 1/4 cup of the dough per cookie. Bake for 12-15 minutes, or until the edges are just starting to become golden brown. Let the cookies cool for about 10 minutes on the baking sheet before transferring to a cool rack and cooling completely before frosting.

In a large bowl, whisk together the powdered sugar, corn syrup, 4 tbs milk, vanilla extract, and salt until the mixture is smooth and drizzle-able. It should be thick, but should still run and be spreadable. If the mixture is too thick, add more milk- too thin, add more powdered sugar.

Pour about 1/2 of the mixture into another small bowl, and whisk in the raspberry jam, adding more powdered sugar if needed. Frost the bottoms of each cookie with half vanilla and half raspberry icing- don't worry if it runs over the edges a little bit!

Let the icing set on the cookies on a cooling rack for about an hour until the frosting has become firm. Enjoy!