Preheat your oven to 350°F. While it heats, prepare your tomatoes by halving them lengthwise—this flat-cut surface will caramelize beautifully and develop deep, concentrated flavor. Pat the cut sides dry with a paper towel to help them roast rather than steam, which is key for getting that sweet, jammy texture.
In a large bowl, combine the olive oil, balsamic vinegar, sliced garlic, sugar, dried oregano, red pepper flakes, and a generous pinch of salt and black pepper. Whisk together to blend the flavors—I find that letting the garlic slivers sit in the oil for just a minute helps them release their aroma before the tomatoes join them. Add the halved tomatoes to the bowl and gently toss to coat all the cut sides evenly with the marinade.
Arrange the marinated tomatoes cut-side down on a rimmed baking sheet (the flat sides should touch the pan for best caramelization). Pour any remaining marinade from the bowl over and around them. Roast at 350°F for 30 minutes until the tomato flesh is soft and the edges begin to caramelize and darken. You'll notice the pan juices will become concentrated and syrupy—these are liquid gold for the final dish.
Transfer the roasted tomatoes to a serving bowl, then carefully pour all the pan juices over them—don't waste a drop of that concentrated, garlicky balsamic glaze. Tear the fresh basil into roughly ½-inch pieces (tear rather than chop to preserve its delicate oils) and gently add it along with the mozzarella pearls. Toss everything together very gently just before serving so the basil stays bright and the cheese doesn't get overworked. I use fresh mozzarella pearls because they melt slightly from the warm tomatoes while staying tender and easy to distribute throughout.