"It also used highly dried brown malt, which gave a roast flavor to the beer. Henry Stopes, a nineteenth-century malting expert wrote in Malt and Malting, of the making of 'brown, blown, snap, or porter malt,' talking about how the porter malthouses .... burnt faggots of beech-wood or oak under the wet malt to dry it, going slowly at first until almost all the moisture has been driven from the malt, then building up the firs so that the sudden violent heat makes the malt grains burst like popcorn."Porters throughout most of the 1700s were brewed entirely from brown malt. From about 1790 on, the recipes called for a declining percentage of brown malt, but it was still a key to the character of porter. In 1817, Daniel Wheeler invented a method of roasting malt at 400 degrees to make a black malt; he took a patent out on the process, and that's where we get "black patent" malt. This made it possible to stain a beer black with only a tiny amount of dark malt--the balance could be made up in brown and pale malts. The percentage of brown malt used in the grist continued to decline over the 19th century as mild ale began to supplant porter.
So, forget that silly recent news about Washington's porter. If you wanted to brew an actual Victorian porter, you'd need to track down some of that funny old brown malt (different, I assume than this brown malt). Or make it. And you'd also need to find a cask somewhere and put the beer in there with some brett* for about a year (or more) if you wanted the really authentic stuff.
*As Osh points out in comments, this is an unnecessarily oblique reference. I've been swimming in this stuff lately, and I forget not everyone is looking over my shoulder and absorbing the same things. This refers to the wild yeast brettanomyces, which was resident in wooden vats of British beer until sometime in the 20th century. It actually takes the name from Britain ("brett"), where scientists first isolated it. It takes awhile to kick in, so beer aged briefly or not at all ("mild" or "running") would have been unaffected.