Pulse together 1 1/2 cups of the flour, 10 tablespoons of the butter and the salt in a food processor. While pulsing, add just enough water for the dough to come together. Remove to a counter and knead a couple times. Wrap in plastic wrap and chill for 20 to 30 minutes.
Remove the dough from the fridge and cut into four pieces. Roll out into 10-inch rounds on floured parchment paper and slide onto parchment-lined baking sheets.
In a small mixing bowl, stir together the ground almonds, granulated sugar and the remaining 3 tablespoons flour. Sprinkle the mixture over the pastry rounds.
In a medium mixing bowl, sprinkle the sliced pluots with some granulated sugar and half of the apple mint and toss. Place the pluots in the middle of each pastry round and gently fold the pastry up and around the fruit. Brush the top and edges of the dough with some egg wash and sprinkle with turbinado sugar. Dot the pluots pieces of the 2 tablespoons butter.
Place in the oven and bake for 15 minutes, or until the crust is golden brown and the bottom is cooked through.
While the galettes are baking, melt the plum preserves in a small saucepot, just to soften. Brush the melted preserves on the crusts as soon as the galettes come out of the oven, and sprinkle with the remaining apple mint.
Whip the cream with an electric mixer. Add a sprinkle of superfine sugar and a dash of calvados and mix in.