Preheat a grill or grill pan to medium. Thickly slice 1 red and 2 yellow onions. Brush the onions and 6 thick slices of rye bread with 1/4 cup extra-virgin olive oil. Grill, turning once, until the bread is toasted, about 5 minutes, and the onions are very tender, about 10 minutes. In a bowl, toss the onions with 1/3 cup chopped parsley; season with salt and pepper. In a small bowl, combine 3/4 cup sour cream and 2 tablespoons dijon mustard. Spread the mixture on the toasts and top with the onions. Sprinkle with 1 1/2 cups grated gruyere cheese and place on the grill. Cover and cook until the cheese is melted, 3 to 5 minutes. Top with more chopped parsley.