1. Heat oven to 350 degree F.
2. For the blueberry compote, combine blueberries, 1/4 cup sugar and lemon juice in a medium saucepan and bring to a boil over medium-high heat. Add 3 tablespoons butter and cook 3 to 5 minutes more, or until some berries have popped and juice is slightly thickened.
3. Bake nuts on jelly-roll pan until toasted, 8 to 9 minutes, stirring once. Cool completely. Process cooled almonds and 2/3 cup sugar in food processor until finely ground.
4. On flat surface, cover phyllo sheets with a lightly dampened clean kitchen towel. Remove 1 phyllo sheet and place it lengthwise in front of you; brush with melted butter. Sprinkle with 3 tablespoons almond sugar. Repeat process with 3 more sheets phyllo, arranging each sheet directly on top of first sheet, buttering and sprinkling each layer with 3 tablespoons almond sugar.
5. Line a large cookie sheet with parchment paper. Cut phyllo stack into fifteen 3-inch squares; discard trimmings. Transfer squares with spatula to prepared sheet. Carefully place another cookie sheet directly on top of squares so the sheets bake flat. Bake 12 to 14 minutes, until lightly browned. (Check squares at 12 minutes by lifting top cookie sheet with potholder.) Transfer stacks to wire rack; cool completely.
6. Meanwhile, prepare another phyllo stack with remaining 4 sheets phyllo, butter, and almond sugar. Repeat cutting stack into squares. Bake and cool completely.
7. Place a jelly-roll pan in freezer until cold, about 15 minutes. Using a 1-1/2 to 2-1/4-inch ice cream, place 20 scoops of ice cream on cold pan. Cover with plastic wrap and return to freezer until ready to use.
8. To serv, arrange 1 phyllo square on each of 10 serving plates. Top each with scoop of ice cream, then 1 heaping tablespoon of Blueberry Compote. Repeat with another phyllo squares, ice cream and 1 heaping tablespoon compote. Cover each with remaining phyllo squares. Serve immediately. Makes 10 servings.