Greek Mixed Greens Pie With Phyllo Crust

to 1/2 cup olive oil, plus more for the baking dish

thick/large scallions, white and light-green parts, trimmed and chopped (1/2 cup)

frozen chopped spinach, kale and/or collard greens, defrosted and squeezed dry (preferably a mix)

crumbled feta cheese

low-fat cottage cheese

large eggs, lightly beaten

finely chopped fresh dill

finely chopped flat-leaf parsley

kosher salt

freshly ground black pepper

sheets (about 8 ounces) phyllo dough, at a cool room temperature