In a medium saucepan over medium-high heat, combine fresh blueberries, sugar, lemon juice, and lemon thyme. Stir until it begins to boil, then reduce heat and simmer for about 10 minutes or until thickened.

Take thick slices of bread and spread a layer of the cooled blueberry compote on one side of each slice. Sprinkle shredded white cheddar and mozzarella over the compote, and top with another slice of bread, compote side down.

Preheat a non-stick skillet over medium heat and melt butter. Place two assembled sandwiches in the skillet, cover with a lid, and grill for about 2-3 minutes until golden brown. Flip sandwiches and continue cooking for another 2-3 minutes.

Remove sandwiches from skillet, let them rest for a minute, then cut in half to reveal the gooey cheese and blueberry compote. Sprinkle with flaky sea salt and thyme before serving.