Cut the chilled Brie into thin slices, place them on wax paper and refrigerate. Preheat the broiler.
Toast the bread, then butter the slices on 1 side. Place 8 pieces of the toast, buttered side down, on a baking sheet; set aside the remaining 4 pieces of toast. Arrange tomato slices on 4 of the pieces of toast on the baking sheet and place a layer of spinach leaves on the other 4 pieces of toast on the baking sheet. Cover the tomatoes and spinach with the chilled Brie slices.
Broil the 8 toasts until the cheese melts. Meanwhile, spread the mustard on the 4 reserved toasts. Remove the toasts from the broiler. Using a spatula, transfer the spinach toasts onto the tomato toasts, then top with the remaining mustard toasts. Slice the sandwiches in half and serve.