Preheat your oven to 350°F (175°C) and line your baking sheets with parchment paper.
In a large mixing bowl, cream together the softened butter, granulated white sugar, and powdered sugar using an electric mixer. Beat until light and fluffy, about 3-4 minutes.
Add the vegetable oil, almond extract, and eggs to the creamed mixture. Mix until well combined, scraping down the sides of the bowl as necessary.
In another bowl, whisk together the all-purpose flour, whole wheat flour, baking soda, salt, and cream of tartar. Gradually add to the wet ingredients, mixing until just combined.
Gently fold in the coarsely chopped almonds and butter toffee baking bits into the cookie dough.
Using a cookie scoop, portion out the dough and roll into balls. Roll each ball in the additional granulated white sugar to coat.
Place the sugar-coated cookie balls on the prepared baking sheets, spacing about 2 inches apart. Bake for 10-12 minutes until the edges are lightly golden, but the centers are still soft.
Remove from the oven and let cool on the baking sheets for about 5 minutes before transferring to a wire rack to cool completely.
