Preheat your oven to 350°F (175°C).
In a large mixing bowl, combine the softened unsalted butter, granulated sugar, and sifted powdered sugar. Using an electric mixer, cream the mixture until it’s light and fluffy, about 2-3 minutes.
Add the vegetable oil, eggs, and almond extract to the creamed mixture. Beat until fully combined.
In a separate bowl, whisk together the all-purpose flour, baking soda, salt, and cream of tartar.
Gradually add the dry mixture to the wet ingredients, mixing on low speed until just combined.
Using a spatula, gently fold in the sliced almonds and almond toffee bits until they are evenly distributed throughout the dough.
Scoop tablespoons of dough and roll them into balls. Roll each ball in the additional sugar to coat.
Place the cookie dough balls on baking sheets lined with parchment paper, spacing them about 2 inches apart. Bake in the preheated oven for 10-12 minutes or until the edges are lightly golden.
Once baked, remove the cookies from the oven and allow them to cool on the baking sheets for about 5 minutes before transferring them to a cooling rack to cool completely.