Combine blueberries, balsamic vinegar, honey and water in a small saucepan. Simmer over medium-low heat for 8 to 10 minutes, crushing some berries and stirring often, until thick and jamlike with little free liquid.
Spread compote on a small plate and cool for 5 minutes so it stops steaming. Spread mascarpone thinly over the inner faces of 2 bread slices.
Add half the cheddar, divide the compote evenly over it and add remaining cheddar. Close with the other bread slices.
Butter the outside faces and cook in a large skillet over medium-low heat for 4 to 5 minutes per side until golden and the cheddar melts, covering for 2 minutes after turning.
Rest for 1 minute, cut carefully and serve one sandwich per person.