Preheat the oven to 400 degrees F (200 degrees C). Grease a 2-quart baking dish with 1 tablespoon butter.
Bring water, 1/2 cup sugar, and cornstarch to a low boil, stirring constantly, in a saucepan. Add strawberries and basil and stir to coat. Transfer mixture to the prepared baking dish. Cut 1 tablespoon butter into pieces; dot on tops of strawberries.
Unravel crescent rolls and rip into pieces, arranging them on top of strawberries as desired, adding as little or as much as you'd like. Melt remaining tablespoon butter in a microwave in a microwave-safe dish, about 10 seconds. Brush melted butter over crescent rolls. Sprinkle 1 tablespoon sugar and cinnamon on top.
Bake, uncovered, in the preheated oven until bubbly and golden, about 25 minutes, covering with aluminum foil for the last 5 minutes to prevent overbrowning.