Walnuts are a great ingredient in brownies, but they can bring with them quite a few grams of fat. So to get some of that walnut flavor without a lot of fat, we used walnut oil instead. For a relatively small amount of oil (only 1/2 teaspoon per brownie), the brownies have a nice nutty undertone. The toasted-nut flavor of the oil makes the brownies seem rich even though they have less than 4 grams of fat apiece. As a side benefit, walnut oil is a good source of alpha-linolenic acid, which is a precursor to heart-healthy omega-3 fatty acid.