In a 4-quart heavy saucepan over moderate heat, bring the blueberries, 1/4 cup sugar, cornstarch and a pinch of salt to a boil. Lower the heat and simmer 3 to 4 minutes, stirring occasionally. Transfer to a medium bowl and let cool completely.
Preheat the oven to 400 degrees F. Butter a sheet pan.
Cover the phyllo sheets with a piece of plastic wrap and a damp paper towel.
Arrange 1 sheet of phyllo on a work surface with the short side nearest you (keep the remaining sheets covered) and brush with some butter. Top with 2 more phyllo sheets, brushing each sheet with butter. Place a heaping 1/4 cup blueberry mixture over the lower third of the buttered phyllo, leaving a 2-inch border along the bottom and sides. Fold the bottom edge of the phyllo up over the blueberry mixture and fold in the sides to enclose the filling completely. Roll up the phyllo to form a strudel, about 4 by 2 inches. Transfer, seam-side down, to the prepared sheet pan. Brush the top with some butter and sprinkle with sugar. Using a paring knife, cut 2 vents across the top of the strudel. Repeat with the remaining ingredients.
Bake until golden brown and crisp, 15 to 20 minutes. Transfer to a rack and cool 20 minutes. Serve immediately.
Recipe courtesy Claire Robinson, 2010