Heat a medium skillet and add the butter. When the butter melts, add the peaches and 1/4 cup sugar. Stir to blend and cook for 1 minute. Remove the skillet from the heat and add the orange liqueur. Return the skillet to the heat and cook the peaches over medium heat until they are tender when pierced with the tip of a knife, 1 to 2 additional minutes. Transfer the peaches to a platter and spread them out. They will cool more quickly that way. Refrigerate so they cool completely.
In the bowl of an electric mixer fitted with the whisk attachment (or, alternatively, with a whisk by hand) whip the cream until it forms soft peaks. Whisk in the remaining 3 tablespoons sugar and the vanilla. Whip until fairly firm in texture. When the peaches are cooled, fold them (and any cooking liquid sitting on the platter) into the whipped cream and transfer to a serving dish or individual glasses. Refrigerate until ready to serve.