1. Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
2. In a large bowl, cream together 1 cup of softened butter and 3/4 cup granulated sugar until light and fluffy.
3. Add 1/2 cup vegetable oil and 1/2 cup powdered sugar to the mixture. Mix until well combined.
4. Beat one large egg into the mixture, followed by 1 teaspoon of vanilla extract. Blend until smooth.
5. In a separate bowl, whisk together 2 3/4 cups all-purpose flour, 1 teaspoon baking soda, and 1 teaspoon cream of tartar. Gradually add this dry mixture to the wet ingredients, mixing until a dough forms.
6. To prepare the blueberry filling, combine 2 cups of fresh blueberries, 1/4 cup water, and 2 tablespoons cornstarch in a saucepan. Add granulated sugar to taste. Cook the mixture over medium heat, stirring until it thickens and bubbles. Optionally, add a pat of butter, a squeeze of lemon juice, a dash of cinnamon, and a pinch of salt for extra flavor. Let the filling cool.
7. Using a cookie scoop, portion the dough into small balls and place them on the prepared baking sheet. Use a sugar-coated glass bottom or measuring cup to flatten each dough ball and create a small well in the center.
8. Fill each well with a tablespoon of the cooled blueberry filling. Be careful not to overfill to avoid spilling during baking.
9. Bake the cookies for 9-11 minutes, or until the edges are golden brown and set.
10. Remove the cookies from the oven and allow them to cool on the baking sheet for a few minutes. Then transfer them to a wire rack to cool completely.
11. Serve and enjoy your homemade Blueberry Pie Cookies with family and friends!