In a medium size skillet, heat 1 tablespoon olive oil, then add panko breadcrumbs to the skillet and toast until golden, about 1-2 minutes; set aside.
To the bowl of a food processor, add goat cheese, ricotta, Parmesan, honey, Italian seasoning, salt, pepper and remaining 1 tablespoon of olive oil. Process for 2 to 3 minutes, or until very smooth. Transfer cheese mixture to a heavy-duty zip-top bag.
Cut a thin slice off the top of each tomato, and run a knife along the inside of the tomato in a circular motion to release the inside, then scoop out to remove the core. Save the insides to make pasta sauce or other tomato sauces.
Snip off the corner of the bag and fill each of the tomatoes with 1 to 2 tablespoons of cheese filling. Sprinkle the filled tomatoes with toasted panko breadcrumbs and the fresh basil. Serve immediately.