In a small saucepan combine the chopped Roma tomatoes, brown sugar, balsamic vinegar, thyme, salt and black pepper. Cook over medium-low heat until the tomatoes soften, the liquid evaporates and the mixture becomes jam-like in texture. Allow it to cool fully before using.
In a food processor, blend basil leaves, pistachio nuts, grated Parmesan, garlic cloves, lemon juice, red pepper flakes, salt and black pepper until finely chopped. With the machine running, gradually drizzle in olive oil until you reach a smooth but slightly textured sauce. Set aside.
Season the room-temp chicken breast with oregano, garlic powder, onion powder, salt and pepper. Heat oil in a skillet over medium heat, add the chicken and cook about 6-8 minutes per side until internal temperature registers ~165 °F (74 °C). Add butter near the end, baste the chicken, then let it rest for about 15–20 minutes before slicing thinly.
Slice your ciabatta rolls in half (or arrange 4 slices of bread). On one side spread roughly 3 tablespoons of pesto, on the other around 2 tablespoons of tomato jam. Layer sliced chicken on top of the pesto side, add prosciutto, then mozzarella slices. If you like, drizzle balsamic glaze over the jam side. Then bring the two halves together.
Pre-heat a skillet or grill pan over medium heat with a little oil. Place the sandwiches in the pan and then lay a heavy skillet, weight or press on top. Grill until both sides are golden brown and the cheese has melted. Serve immediately while warm and gooey.