Pour can of plum tomatoes into a bowl and crush with your hands.
Add tomatoes and broth to a medium saucepan and heat through, then reduce to low.
In a large saucepan over medium heat, add olive oil and onion. Sauté until onion is translucent, then add rice and stir briefly to toast. Add white wine to pan, then reduce heat to medium-low and stir until wine has evaporated. Add a ladle full of tomato and vegetable stock mixture to rice, then stir with a wooden spoon until the stock has been absorbed by the rice. Add another ladle full of stock to rice and stir until that has been absorbed. Repeat this process until the rice is al dente, but the dish is extremely creamy. Add in Pecorino, basil, salt and pepper to taste, and stir. Remove from heat.
Transfer to four serving dishes, top each with a quarter of the burrata, a sprig of basil, a few quartered cherry tomatoes, and a drizzle of olive oil.