01 - In a small bowl, gently mash the blueberries with honey or maple syrup and lemon zest until slightly broken down and syrupy. Set aside to allow flavors to 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 for an extra-crispy crust.
03 - Place two slices of bread buttered-side down. Layer each with a slice of sharp white cheddar, spoon the blueberry mixture evenly over the cheese, then top with the remaining cheddar slices. 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 in half and serve immediately while warm and gooey.