Preheat your oven to 350°F (175°C).
In a large mixing bowl, cream together the unsalted butter, granulated sugar, and sifted powdered sugar until light and fluffy.
Add the vegetable oil, eggs, and almond extract to the mixture and beat until well combined.
In a separate bowl, whisk together the all-purpose flour, baking soda, salt, and cream of tartar. Gradually add this to the wet mixture and mix until just combined.
Fold in the sliced almonds and almond toffee bits until evenly distributed.
Portion the dough into balls about 1.5 inches in diameter and roll each in additional sugar.
Place the dough balls on baking sheets lined with parchment paper and bake for 10-12 minutes.
Let the cookies cool on the sheets for 5 minutes before transferring them to a cooling rack.