Umm zero?
Brown sugar and DME are completely different animals. Don't cut corners on the DME. DME is a combination of base malt and roasted malts that have been previously brewed then spray dried into a powder for your brewing pleasure. Depending on the type of DME, there are all sorts of roasty, malty flavors going on in it that Brown Sugar isn't even remotely close to providing. Brown sugar is simply white sugar that's been cooked a little to produce malliard reactions and pre-caramelization flavors. If you try to use brown sugar as a base malt, you're going to wind up with a dry alcoholic failure.
Tell your wife to go to the LHBS and pick up some Amber DME.