Special equipment: a strawberry huller or small melon baller
Put the ginger ale in a saucepan, sprinkle the gelatin evenly over the top and let it absorb the liquid for 2 minutes. Bring the ginger ale just to a boil and whisk until gelatin is fully dissolved. Remove from the heat and whisk in the sugar until dissolved.
Transfer the gelatin to a large bowl and stir in the champagne. Refrigerate until cooled and thickened slightly (almost to the consistency of a gel but still runny-you can check a few times to see), 15 to 20 minutes.
Meanwhile, slice off the bottom tip of each strawberry so there is a flat edge for it to stand upright; be careful to not cut off so much that there is a hole at the bottom once the strawberry is cored.
Use a strawberry huller or small melon baller to core out the strawberry, again, making sure you don't dig so deep that you create a hole in the bottom.
Spoon the champagne mixture into the strawberries and stand them in a baking dish. Refrigerate until firm, about 1 hour. Garnish with mint leaves and serve.