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