Cheese, Leek, and Herb Souffle Casserole

Chives, fresh

Dill, fresh

Parsley, fresh

Eggs, large

All-purpose flour, unbleached

Kosher salt and freshly ground pepper

Gruyere cheese, grated

Parmesan cheese

Whole milk

1 pound large leeks (white and pale-green parts only), quartered lengthwise, cut into 1/8-inch slices (4 cups), and rinsed well

1 tablespoon plus 1 stick unsalted butter, plus more for dish