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Preheat the oven to 350 degrees F.
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In a large bowl, use an electric mixer to combine the sugars, butter and oil until well blended. Add the almond extract and eggs and mix well.
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In separate bowl, whisk together the flours, baking soda, salt and cream of tartar. Add the dry mixture to the sugars and mix at a low speed until well blended.
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Stir in the almonds and toffee bits. Form balls with about 1 tablespoon of dough per ball. Roll in granulated sugar and place 5 inches apart on ungreased cookie sheets. With a fork dipped in sugar, flatten the ball of dough with criss-cross fork pattern.
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Bake for 12 to 18 minutes, until golden brown and crisp.