Combine 2 1/2 tablespoons cornstarch and 1/3 cup milk in a saucepan, stirring well. Add remaining 2 1/3 cups milk, sugar, vanilla, and eggs. Cook over medium heat, stirring constantly, until mixture comes to a boil. Cook, stirring constantly, 2 minutes or until thickened. Cover and chill.
Place 1 sheet of phyllo on a dry surface (keep remaining phyllo covered). Coat with cooking spray. Layer remaining phyllo on first sheet, coating each sheet with cooking spray. Cut stack in half lengthwise; place 1 portion on top of the other, forming 16 layers. Cut stack into 8 squares; transfer to a baking sheet coated with cooking spray. Bake at 375° for 5 minutes.
Separate each phyllo stack, making 6 sheets for bottom layer, 4 sheets for middle layer, and 6 sheets for top. Place bottom layers on individual plates; top each with 1/4 cup custard mixture. Top with middle layer and 1/4 cup custard. Top with remaining layer.
Position knife blade in food processor bowl; add strawberries, and process until smooth. Pour puree through a wire-mesh strainer into a saucepan, discarding pulp. Add 1 tablespoon cornstarch to strawberry puree; stir well. Add jelly, and cook over medium heat, stirring constantly, until thickened. Cook 1 minute. Remove from heat; stir in Cognac. Drizzle over phyllo stacks. Garnish with berries, if desired. Serve immediately.