In a saucepan, warm the stock over medium-low heat. Add the tomato paste and whisk, making sure the tomato paste is fully incorporated into the stock. You will occasionally need to stir the stock before adding to the risotto.
While the stock is warming, start the risotto. In a separate large skillet or braiser, melt 3 tablespoon of butter over medium to medium-low heat and, when melted, add the shallots. Cook gently without browning the shallots until they are translucent. It will take just a minute or two.
Next, add the garlic and cook until fragrant – about 15 seconds. Stir in the rice, making sure it is coated in the butter and turn the heat to medium. Stirring often, let the rice absorb the butter. This will take about 2 minutes. Add the wine and stir and scrape with a wooden spoon, making sure the rice doesn’t stick to the bottom of the pan.
Once the wine has absorbed, add a ladle or two of stock (about ½ cup total) and stir. As the rice absorbs the stock and starts to stick to the pan, add more stock in the same increments and continue to stir. Once you’ve added the stock the second time and it has absorbed, add the black pepper and vinegar and stir well.
Continue adding stock a couple small ladles at a time until about ¾ of the stock has been added (after about 18 minutes of cooking), then stir in the salt and tomatoes. The tomatoes will warm and release some juice, but should remain relatively intact when finished, so don’t add too early. They should be added right before or after the final ladle of stock. After about 20 total minutes of cooking, taste the rice for doneness – it should be firm but not hard – like al dente pasta.
Once the rice is done (approximately 20-25 minutes of cooking), remove it from the heat and stir in the cheese and last tablespoon of butter until melted. Taste for seasoning and add salt if necessary. Stir in the basil and serve.