In a small saucepan, combine the blackberries, sugar, rosemary, lemon juice and salt. Cook over medium heat until the mixture starts to bubble. Reduce the heat to a gentle simmer.

Mash some of the berries with the back of a spoon or fork to help release their juices. Simmer for 10 to 15 minutes, stirring often, until it thickens to a jam-like consistency.

Remove from heat and let the jam cool. It will continue to thicken as it rests.

Lay out all 8 slices of sourdough bread. Spread butter on one side of each slice - this side will face the skillet. Flip the slices so the unbuttered sides face up.

On 4 slices of bread, layer 2 slices of provolone cheese. Spoon a thin layer of the blackberry jam on top, then sprinkle with goat cheese and finish with shredded mozzarella. Top with the remaining bread slices, buttered side facing out.

Heat a large skillet over medium low heat. Place the sandwiches in the skillet and cook for 3 to 4 minutes per side, until the bread is golden brown and the cheese is melted. Serve immediately.