Vegan brownies are just as easy as non-vegan brownies. Take your favorite brownie recipe and simply replace your eggs with approximately 2 tablespoons of water per egg and your butter with oil or applesauce (or vegan margarine). Oil will make your brownies more dense and chewy while applesauce will make your brownies more cake-like. You can also mix some combination of oil and applesauce. Conversion amounts are direct, ie. if your recipe calls for 1/2 cup of butter, use half a cup of oil, applesauce, or margarine.
I <3 raspberries and chocolate so I added just raspberry syrup to my brownie.