Heat a large nonstick skillet over medium heat. Butter four bread slices on one side only. Place slices, butter-side down, on a clean surface. Spread 1/2–1 tablespoon fruit spread or preserves of choice in a thin layer on each slice. Top with cheese and layer with avocado slices. Cover with remaining bread; butter tops.
Place two sandwiches in the pan and cook for 2–3 minutes, until bread is golden brown and cheese has begun to melt. Flip sandwiches over, pressing down slightly with a spatula. Continue cooking until golden brown. Serve immediately.