In a small bowl use a fork to mash together avocado, lemon juice, cumin, and salt until smooth. Stir in parsley. Set aside.
Top four of the bread slices with the cheese. Spread with the avocado mixture and top with tomato slices. Place the remaining bread slices on top of tomato slices. Spread top of the bread slices lightly with half of the butter.
Heat a large nonstick griddle or 12-inch skillet over medium-high heat. Carefully add sandwiches, buttered sides down. Very carefully spread tops with the remaining butter. Cook for 4 to 6 minutes or until golden, turning once.