Butter an 8x8-inch casserole dish.

Use remaining butter to lightly butter bread. Cut each slice in half diagonally. Arrange 1/2 of the bread in the prepared dish. Sprinkle with half of the Swiss cheese, 1/2 of the green onions, 1/2 of the parsley, and 1/2 of the shrimp, in that order. Top with remaining bread and sprinkle with remaining cheese, onions, parsley, and shrimp.

Beat milk, sour cream, eggs, Dijon mustard, and salt together in a bowl. Pour over casserole, cover, and refrigerate for 8 hours, to overnight.

Preheat the oven to 350 degrees F (175 degrees C).

Bake casserole in the preheated oven until puffed and golden, 30 to 40 minutes. Let sit for 5 minutes. Cut into squares and serve.