I'm interested in this recipe for an egg allergy rather than all vegan.

To use butter instead of oil in this salted chocolate cookie recipe, I'd increase the fat by 2 tablespoons + 1 teaspoon, given the standard conversion ratios going the other way. (If you were starting with butter and wanted to use oil, you'd reduce by 20%. Conversely, to go from oil to butter, increase by 25%. Adding 2 tablespoons + 1 teaspoon is not exact, but it's close enough. If you wanted to do the conversion perfectly, it would be 2 tablespoons + 3/4 of teaspoon.).

There is water in butter as well as fat, so I'd probably not add quite as much water as the recipe calls for - holding back a few tablespoons until after making the dough, to see if it's just too dry without the full amount called for, adding more at the end only if necessary. ;o)