Preheat the oven to 425 degrees F.
Unfold the puff pastry sheet and, using a rolling pin, lightly roll the pastry out. Using a sharp knife, cut out a 10-inch round, using a dinner plate as a guide. Transfer the round to a tart pan with a removable bottom.
Sprinkle 1 tablespoon sugar on the bottom of the tart and arrange the fruit wedges over the sugar, packing them in tightly and making 1 big circle. Sprinkle with the remaining 2 tablespoons sugar and with the sliced almonds. Bake until the edges are golden brown, 25 to 30 minutes. Cool on a rack.
Just before serving, heat the apricot jam with 2 tablespoons water in a small pot over moderate heat. Using a pastry brush, paint the tart with the melted jam.
BYOC: Trying serving this with your favorite stone fruit ice cream, such as peach, or with freshly whipped cream.