Preheat oven to 350º. Cut squash into ½” thick slices and arrange on a parchment-lined sheet pan. Rub 1 T olive oil over squash and sprinkle with a pinch of salt and pepper. Roast 10 min. Toss shallots in remaining 2 T olive oil to coat and add to pan, cooking 7-8 min more until squash is softened when pierced. Remove from oven and reserve.
Meanwhile, sauté pancetta in skillet over medium heat just until edges are beginning to crisp, approx. 3 min; remove from heat and reserve.
Make white balsamic drizzle by combining vinegar, extra virgin olive oil, sugar and pinch of salt and pepper. Set aside.
Place puff pastry on a dry, lightly floured work surface. Gently roll back and forth top to bottom a few times with a rolling pin to lengthen the sheet. Trim a very thin bit of dough away from each side to get a better rise and uniform shape (more dough may be removed to fit desired serving size, as needed). Transfer dough to a parchment-lined baking sheet. Brush dough generously with beaten egg. Arrange squash slices on pastry, being careful not to crowd or overlap; add pancetta and walnuts, season very lightly with salt and pepper and bake 10 min. Remove from oven and add shallots and crumbled cheese in large pieces. Bake 7-10 min more until edges are fully puffed and golden. Remove from oven, add vinegar drizzle over entire tart to moisten, garnish with chervil leaves and serve immediately with a green salad and white wine, if desired.