Strip Swiss Chard leaves from stems. Roughly chop stems into 1 inch pieces, set aside. Roughly chop leaves into 1 inch strips.
Add butter and oil to a deep pan set over medium heat. When butter foams add shallots and swirl. Add chopped stems and when they start to soften (2 mins or so) add white wine. Wait 1 more minute and add leaves stirring well so that they wilt evenly and then turn off the heat. Cover for another 1-2 minutes. You want it to be green but soft like spinach – if you leave it cooking or covered too long it will turn green/brown.