In a large bowl, whisk together the flour, cream of tartar, baking soda and salt. Set aside.
2 1/4 cups (281 grams) flour, 1/2 teaspoon cream of tartar, 1/2 teaspoon baking soda, 1/2 teaspoon salt
In another large mixing bowl with an electric hand mixer, beat together the butter, oil, granulated sugar and powdered sugar until well blended.
1/2 cup (113 grams) unsalted butter, 1/2 cup (99 grams) vegetable oil, 1/2 cup (100 grams) granulated sugar, 1/2 cup (60 grams) powdered sugar
Add the egg, lemon zest, and lemon extract and beat until fully incorporated.
1 large egg, 2 tablespoons lemon zest, 1 teaspoon lemon extract
Gradually beat in the dry mixture to the wet mixture, mixing just until combined. Be careful not to overmix; the dough should be light and fluffy. It’ll be too wet to form into balls at this point.
Chill for at least 6 hours. Overnight or 2-3 days also works.
Line a baking sheet with a piece of parchment paper. Preheat the oven to 375 °F.
Place the raw sugar in a small bowl.
3 tablespoons raw sugar
Roll the dough into 24 30-gram balls.
Roll into the raw sugar and place the balls on the prepared baking sheet. Don't press down!
Bake for 8-12 minutes or until the top center no longer looks wet.
Remove from the oven and use the back of a 1-teaspoon measuring spoon to create an indentation. I pressed down almost all the way (but don't break through the cookie!).
Fill with about 1/2 to 3/4 teaspoon jam.
3-4 tablespoons raspberry jam
Put back in the oven and bake for another 4-7 minutes. They'll have crackled a bit.
Remove from the oven and let cool completely on the baking sheet, about 2 hours.
Mix the powdered sugar with the lemon extract and gradually add 1-2 tablespoons of milk until you achieve a drizzling consistency.
1/2 cup (60 grams) powdered sugar, 1/4 teaspoon lemon extract, 1-2 tablespoons milk
Pipe over the cookies. Let the icing harden for about 2 hours or until firm. If you're in a hurry, you can refrigerate them.