Preheat oven to 350°. In a large bowl, cream butter and sugars until blended. Add 1 egg at a time, beating well after each addition. Gradually beat in oil and extract. Combine the flour, baking soda, cream of tartar and salt; gradually add to the creamed mixture and mix well. Stir in almonds and toffee bits.
Drop by teaspoonfuls 2 in. apart onto ungreased baking sheets. Bake until golden brown, 10-12 minutes. Remove to wire racks to cool.