Have ready 4 sheets of plastic wrap. Place 3 generous scoops of ice cream on each sheet; gather ends lengthwise and mold into the shape of a baked potato. Set each on a sheet of aluminum foil and wrap to hold in place; transfer to freezer to firm, about 1 hour. Repeat 3 more times.
In the bowl of an electric mixer fitted with the paddle attachment, cream butter and sugar until light and fluffy; mix in yellow food coloring. Using an offset spatula, spread yellow butter 1/4 inch thick on a parchment-paper-lined baking sheet; freeze for 20 minutes. Cut into 1-inch "butter pats," and set aside.
Unwrap frozen "potatoes," and coat with cocoa powder. Draw a knife through the cocoa on top of each "potato" to expose the inside. Top with whipped cream, green sprinkles for "chives," and "butter pats." Serve immediately with chocolate sauce.