01 - In a small bowl, gently mash the blueberries with honey or maple syrup and lemon zest until slightly chunky. Set aside to let the flavors meld.
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 bread slices buttered side down. Layer each with one slice of sharp white cheddar, spoon the blueberry filling 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 has fully melted.
05 - Remove the sandwiches from the skillet and let rest for 1 minute. Slice each in half diagonally and serve immediately while warm and crisp.