Heat nonstick griddle over medium heat. Brush one slde of each bread slice with melted butter.
Place one slice buttered bread buttered side down on grill. Sprinkle 1 tablespoon cheddar over bread. Add ricotta and blueberries, keeping both away from the edges. Sprinkle on remaining cheddar. Top with remaining buttered slice.
Grill first side until golden brown and cheese starts to melt. Flip sandwich and grill until second side is golden brown and cheese melted.