Beat 1/3 cup superfine sugar and butter together in a bowl with an electric mixer until light and fluffy, about 5 minutes. Add eggs yolks and beat well; beat in almond extract. Stir ground almonds and flour into butter mixture until mixture has a thick paste-like consistency.
Cut puff pastry into 8 equal pieces. Place 1 tablespoon almond mixture in the lower center of each piece. Fold top of puff pastry down over the filling and press edges together to seal. Make three 1/2-inch cuts equal lengths apart on the bottom edge to make the "claws". Transfer pastries to a baking sheet.
Whisk egg and water together in a bowl. Brush each bear claw with egg mixture and sprinkle with remaining 2 tablespoons superfine sugar and sliced almonds.
Bake in the preheated oven until puffed and golden brown, 15 to 20 minutes.