Whisk the prosecco and sugar in a saucepan until combined. Sprinkle the gelatin over the top, allowing it to sit for a few minutes. Heat the mixture over medium-low heat until the gelatin is dissolved and the liquid just starts to simmer. Remove the saucepan from the heat and whisk in the peach nectar.
Pour the mixture into an 8-by-8-inch baking dish (or something even smaller for thicker shots!). Drop the peach slices into the dish; they will float to the top. Refrigerate the dish until set, 2 to 3 hours. Slice into squares. I also like to slice these into cubes and serve in champagne glasses!