01 - In a small bowl, gently mash the blueberries with honey (or maple syrup) and lemon zest until slightly combined but still chunky. Set aside.
02 - Spread softened butter evenly on one side of each bread slice. If using Parmesan, press the buttered sides into the grated Parmesan to coat lightly.
03 - Place two slices of bread buttered-side down. Layer each with one slice of sharp white cheddar, spoon the blueberry mixture evenly over the cheese, then top with another slice of cheddar. Cover with the remaining bread slices, buttered-side facing outward.
04 - Heat a large skillet or griddle over medium-low heat. Place the assembled sandwiches in the skillet and cook for 3 to 4 minutes per side, pressing gently with a spatula, until the bread is deeply golden and the cheese is fully melted.
05 - Remove the sandwiches from the skillet and let rest for 1 minute. Slice each sandwich in half and serve immediately while warm.