1. In a large nonstick skillet, melt the butter. Add the squash and 1 cup water and simmer over medium heat; season with salt and pepper. Cook, stirring, until the water is evaporated and the squash is golden and tender, about 13 minutes; set aside.
2. Position a rack in the upper third of the oven and preheat to 400°F . Meanwhile, lightly grease an 8-inch square glass baking dish and spread 1/2 cup white sauce in the bottom. In a bowl, whisk together the pumpkin puree and egg.
3. Cut half of the egg roll wrappers into 3 strips each. Fill a large bowl with hot tap water (as you work with the wrappers, dip them in the water to rinse off the starch). Use 1 whole wrapper and 3 strips to cover the bottom of the dish in a single layer (there will be overlap). Spread a generous 1/2 cup of pumpkin mixture on top and sprinkle with 1/3 cup cheese. Repeat the layering.
4. Add another layer of egg roll wrappers. Spread with 1 cup white sauce, then top with the squash, basil and 1/3 cup cheese.

White Sauce:
Melt butter in medium saucepan over medium heat. Add shallots and cook until tender, about 5 minutes. Stir in flour for 2 minutes. Gradually whisk in warm milk; bring to boil and cook for 2 minutes, whisking constantly. Remove from heat and stir in parmesan and 1/4 tsp. each salt and pepper.

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