Caramelized Zucchini Phyllo Pie

Thaw 1 (1-pound) package phyllo dough overnight in the refrigerator, if needed (if there are two interior packages, just thaw one). Unroll and stack 6 of the phyllo sheets on a large baking sheet. Cover with plastic wrap, wax paper, or a damp kitchen towel and leave at room temperature. Reroll the remaining phyllo sheets, place in a gallon-size zip-top freezer bag, and refreeze for another use.

Trim the ends off 1 1/2 pounds zucchini. Slice each in half crosswise, then halve lengthwise. Slice lengthwise into thin planks. Place in a large bowl. Halve and thinly slice 2 shallots. Add to the bowl with the zucchini.

Heat 3 tablespoons of the olive oil in a 10-inch cast iron or straight-sided ovensafe skillet over medium-high heat until shimmering. Add the zucchini and shallots (reserve the bowl), season with 1 1/2 teaspoons of the kosher salt and 1/4 teaspoon of the black pepper, and toss to coat in the oil as best you can (the pan will be very full).

Cook, stirring occasionally, until the squash and shallots are slightly caramelized and beginning to stick to the pan, 12 to 15 minutes. Reduce the heat to medium, add 1 tablespoon water, and continue to cook 5 minutes more, scraping up the flavorful stuck-on bits as you go.

While the squash cooks, arrange a rack in the lower third of the oven and heat the oven to 400°F. Whisk 2 large eggs in a large bowl. Prep and add the following to the bowl: Coarsely chop fresh basil leaves until you have 1/4 tightly-packed cup. Coarsely chop fresh dill until you have 3 tablespoons. Finely grate Parmesan cheese until you have 1 scant cup, if needed. If using fresh corn, remove the husks and cut the kernels from the cobs (about 1 1/2 cups). Crumble in 3 ounces feta cheese. Season with the remaining 1/2 teaspoon kosher salt and 1/4 teaspoon black pepper.

When the squash is ready, add it to the bowl and stir to combine. Pour the remaining 2 tablespoons olive oil into a small bowl, for brushing. Wipe the skillet clean and brush with a thin layer of the oil.

Working quickly to prevent the phyllo from dying out, transfer 2 phyllo sheets to the skillet, overlapping them to completely cover the bottom and sides of the pan, folding any overhang into the pan. (Keep the remaining phyllo covered). Brush lightly with olive oil. Place a third phyllo sheet in the skillet so that half is hanging over the rim. Repeat with the remaining 3 sheets, arranging them so they completely cover the rim of the skillet.

Spread the zucchini mixture into the skillet in an even layer. Fold and crimp the overhanging phyllo toward the center, leaving the center 4 inches exposed. Gently brush any remaining oil over the phyllo.

Bake until the phyllo is golden brown and crispy and the center is slightly puffed and set, 25 to 30 minutes. Let sit 10 minutes before slicing. Top with torn fresh basil leaves. Serve with hot sauce, if desired.