In a food processor, combine 2 1/2 cups flour, butter, 1 teaspoon sugar, and salt; pulse until mixture resembles coarse meal. Sprinkle with 1/4 cup ice water. Pulse until dough is crumbly but holds together when squeezed (if necessary, add up to 1/4 cup remaining ice water, 1 tablespoon at a time). Dont overmix. Remove dough from processor and shape into a disk; wrap in plastic and refrigerate 1 hour. Meanwhile, wipe bowl of food processor clean and add almonds, 3 tablespoons sugar, and 2 tablespoons flour; pulse until ground to a coarse meal.
Preheat oven to 350 degrees. On a floured surface, roll out dough to 1/4-inch thickness. Transfer to a parchment-lined baking sheet; sprinkle almond mixture over dough. With a spatula, transfer plums to dough; press lightly to fan out, leaving a 2-inch border. Fold edge of dough over fruit. Refrigerate 20 minutes. Brush crust with cream; sprinkle galette with 2 tablespoons sugar. Bake until crust is golden and underside is cooked through, about 70 minutes.