Combine 1/2 cup sugar and cornstarch in a small saucepan; gradually stir in water until smooth. Stir in blueberries and lemon juice; bring to a boil. Reduce heat to low and simmer, uncovered, until slightly thickened, about 5 minutes. Cover and refrigerate until chilled, about 30 minutes.
Preheat oven to 350 degrees F (175 degrees C).
Combine graham cracker crumbs, 2 tablespoons sugar, and cinnamon in a large bowl; stir in butter. Pat into ungreased 10x15-inch baking pan.
Bake crust in preheated oven until lightly browned, 10 to 15 minutes. Cool completely on a wire rack, then crumble crust.
Whisk 1 1/2 cups sugar, pudding mix, whipping cream, milk, and vanilla extract in a large bowl. Fill ice cream freezer cylinder two-thirds full. Freeze according to manufacturer's directions; refrigerate remaining mixture until ready to freeze. Whisk remaining mixture before placing in cylinder to get rid of lumps.
Layer ice cream, graham cracker mixture, and blueberry sauce three times in a large bowl; swirl to combine. Freeze until ready to serve.
