Butternut Squash Pie with Shallots, Radicchio, and Feta

box (17.3 ounces) frozen puff pastry, both sheets thawed according to package directions

unbleached all-purpose flour, for dusting

medium (roughly 2 and 1/2 lbs) butternut squash, peeled, seeded, and chopped into 1-inch chunks

medium shallots (roughly 8 ounces), sliced into quarters

sprigs fresh rosemary (optional)

extra virgin olive oil

kosher salt

freshly ground black pepper

small head radicchio (roughly 8 ounces), thinly sliced

balsamic vinegar

crumbled feta cheese

large egg, beaten

milk