Heat the olive oil in a Dutch oven over medium-low heat. Add the garlic, about half of the cherry tomatoes, and salt and cook, stirring occasionally, until the tomatoes start to break down, about 3 minutes. Add half of the fresh basil and all of the chili flakes, if using, and cook until the basil is wilted, about 30 seconds.
Add the orzo and broth and increase the heat to medium-high. Bring to a simmer. Once simmering, cover with a lid, reduce the heat to low, and cook, stirring and scraping the bottom of the pot occasionally, until the orzo is tender and most of the liquid has been absorbed, about 10 minutes.
Remove the pot from the heat and season the orzo to taste with salt and pepper. Stir in the remaining basil and tomatoes and the fresh mozzarella. Serve immediately with a drizzle of fresh olive oil and balsamic vinegar, if desired.
