You've Got Some Room to Improvise
Sour cream might not be the first thing that comes to mind when you think of low-fat baking ingredients, but when you're using it to replace oil--which is all fat--that's exactly what it is. It's a simple stir-in substitution, whether you're baking from scratch or a commercial brownie mix. The finished brownies are just as decadently rich and chocolate-y, but with less fat and, surprisingly, even bit of added nutrition from the stealthy dairy product.
Sour Cream With a Boxed Mix
Sour cream contains both fat and moisture, which makes it an easy substitute for the oil and water called for in a boxed brownie mix. Instead of using the quantities of oil and water called for on the box--typically a half-cup of oil and a quarter-cup of water, though there's variation between brands--simply add the total amount of those two ingredients and replace that full amount with sour cream. The brownies will mix and bake as they normally would, though the batter might feel slightly stiffer than usual.
Sour Cream in a Scratch Recipe
You can substitute sour cream for oil in scratch brownie recipes as well. This is slightly more complicated, because from-scratch recipes are more variable, but it's still pretty easy. As a rule you can substitute sour cream for up to 3/4 of the oil called for in your recipe, without affecting its texture significantly. If your recipe called for 1/2 cup of oil, for example, you'd use 3 fluid ounces of sour cream and then top it up with the remaining ounce of oil. Alternatively, instead of making the substitution, look online for brownie recipes that already incorporate sour cream. It adds richness and a chocolate-enhancing tang to the batter, so many recipes treat it as a "secret ingredient" intended solely to make them taste better.
What You Get
As substitutions go, swapping out oil for sour cream is one of the better trades from a nutritional perspective. A cup of vegetable oil packs a whopping 1,927 calories, and very little else. By contrast even full-fat sour cream has under 500 calories and reduced-fat sour cream has 327 per cup, so that's an immediate advantage. Better yet, the sour cream packs protein and calcium, other minerals including potassium and phosphorous, and a number of vitamins as well. Their nutritional value is probably the last thing you're thinking about when you bite into a brownie, but it's a clear reason to opt for a sour-cream brownie recipe.
If sour cream isn't something you keep on hand, you can opt for other substitutions. Thick, plain Greek yogurt is probably the closest equivalent to sour cream, though it's even lower in fat. As with sour cream, use it to replace up to 3/4 of the oil in your brownies, rather than all of it, for the best results. The same holds true for applesauce, another longtime standby in low-fat baking, which is also vegan-friendly. Soft or silken tofu and mashed-up avocado can work as well, though they're best used for no more than half the fat as they yield a drier brownie. You can compensate for that by using sour cream, yogurt or applesauce for the other half, replacing the moisture but still keeping the brownie's fat content very low.