Special equipment: 4 dessert cups and liquid nitrogen or an ice cream maker
For the sugar cookie dough: Combine the butter, flour, sugar, egg yolk, lemon zest and salt in the bowl of a food processor. Pulse together, adding a few splashes of ice water to make it come together. Shape the dough into a disc, wrap it in plastic and let it rest in the fridge for at least 30 minutes.
Preheat the oven to 375 degrees F.
Cut the rested dough in half and roll out each piece to about 1/4 inch thick. Sprinkle the turbinado sugar over the dough and lightly roll over it to set it in place. Cut out 8 shapes using a round cookie cutter. Place on a sheet tray and bake until light golden, about 8 minutes. Let cool.
For the sweetened mascarpone: Mix together the mascarpone, sugar and lemon zest and juice in a medium bowl until smooth and silky. Place in a piping bag and refrigerate until ready to use.
For the ruby red grapefruit and prosecco sorbet: Combine the grapefruit juice, prosecco and sugar in the bowl of a stand mixer fitted with a whisk attachment. Mix on medium speed while carefully pouring in liquid nitrogen. Pour in enough nitrogen until you achieve a sorbet-like consistency. Place the bowl in the freezer until ready to use. Alternatively, pour the grapefruit mixture into an ice cream maker and process according to the manufacturer¿s instructions.
Combine the satsuma, orange and grapefruit segments in a large bowl. Pipe some sweetened mascarpone into the bottom of 4 dessert cups. Top with the citrus segments and a scoop of the ruby red grapefruit and prosecco sorbet. Tuck two cookies in each glass and garnish with the mint.