In a saucepan over medium heat, combine halved cherry tomatoes, granulated sugar, apple cider vinegar, a pinch of salt, and red pepper flakes. Stir together and cook for 20-25 minutes until syrupy.

Remove from heat and let the jam cool while you prepare the other components.

In a food processor, combine fresh basil leaves, toasted pine nuts, grated Parmesan cheese, and minced garlic cloves. Pulse until finely chopped.

While the processor is running, drizzle in olive oil until reaching a smooth texture. Season with salt and pepper.

Preheat a skillet over medium-low heat. Spread softened butter on one side of each slice of sourdough bread.

On the non-buttered side, spread pesto, add the mozzarella and cheddar cheeses, then spoon on some tomato jam. Top with another slice of bread, buttered side out.

Cook the sandwiches in the skillet for about 3-4 minutes on each side, pressing gently with a spatula for even browning.

Remove when the bread is golden brown and cheese is melting.

Once golden and toasted, remove from skillet and cool for a minute before slicing. Serve immediately.