Preheat your oven to 350°F (175°C) to ensure even baking.
In a large mixing bowl, combine the softened butter, granulated white sugar, and powdered sugar. Beat until light and fluffy—about 3-5 minutes.
Add the vegetable oil, almond extract, and eggs. Beat until fully incorporated.
In a separate bowl, whisk together the all-purpose flour, whole wheat flour, baking soda, salt, and cream of tartar.
Gradually add the dry ingredients to the wet mixture, beating on low speed until just combined.
Fold in the coarsely chopped almonds and butter toffee baking bits using a spatula.
Using a cookie scoop or spoon, portion out the cookie dough and roll into balls. Roll each ball in granulated sugar to coat.
Place the cookie dough balls on prepared baking sheets, leaving space between each. Bake for 10-12 minutes until edges are lightly golden.
Allow cookies to cool on baking sheets for about 5 minutes before transferring to a cooling rack.