Heat a 12” skillet over medium heat for 2 minutes. Add the ghee and swirl to coat. Add the tomatoes to the skillet along with 1/2 teaspoon salt. Cook until tomatoes are turning golden brown on 1 side – about 5 minutes. Stir and continue to cook for 2 more minutes. Some of the tomatoes will begin to burst.
Mince the garlic with 1/4 teaspoon of sea salt to form a smooth paste. Transfer to a large bowl and add the olive oil, vinegar, thyme, lemon juice, pepper flakes, paprika and 1/2 teaspoon salt. Whisk to combine. Add the roasted bell pepper and charred tomatoes. Stir to combine and let sit for about 30 minutes to allow the flavors to meld.
Add the basil and bocconcini and toss to combine. Serve at room temperature.