In a medium bowl, sprinkle gelatin over 3 T cold water and set aside 5 minutes.
Whisk melted chocolate into gelatin, then mix in warm milk and smoked paprika.
Whip cream until it forms medium-stiff peaks then fold ⅔ of it into chocolate mixture. Whisk in Chobani and refrigerate until set, about 30 minutes.
Whisk to loosen the mixture (it will start out grainy and will smooth out as you whisk). Combine confectioners’ sugar and remaining whipped cream and serve over mousse.