Preheat the oven to 425°F. Line a rimmed sheet pan with parchment.
Add tomatoes to the pan. Drizzle with olive oil and balsamic.
Sprinkle on garlic, salt, pepper, thyme, and red pepper flakes. Toss to coat evenly.
Spread tomatoes in a single layer. Roast until blistered and jammy, about 18–20 minutes.
For extra char, broil 1–2 minutes, watching closely.
Fold in basil on the hot pan. Sprinkle Parmesan if using. Rest 3 minutes before serving.