Butter a 3-quart gratin dish or casserole pan.
Slice the scallions or leek. Shave the corn from the cobs. Chop the parsley and basil.
Cube the bread. If it isn’t dry, then lightly dry it by heating it in a 200F oven on a cookie sheet for 10-20 minutes.
Heat the oil in a wide skillet over medium-high heat. Add the scallions or leek, the corn, and paprika or chile. Cook until the scallions have softened and the corn is heated through, about 4 minutes.
Season with 1/2 teaspoon salt and stir in the parsley and basil.
Whisk the eggs and milk with 1/2 teaspoon salt and pour it over the bread cubes in a bowl. Add the corn mixture and grated cheese.
Transfer the mixture to the prepared dish. Pour over the half-and-half.
Bake until puffed and browned, about 45 minutes.