In a large stock pot over medium hight heat, add the tomatoes and using a spatula, break them up a bit. These will cook for an hour and a half, or so, until it becomes a rich, thick tomato paste that we will use for the risotto. This must happen before you even think about risotto. You can make this the day ahead.
Once you have the tomato paste ready to go, get started. In the same pot you made the paste (if it's dirty, it's fine) add the olive oil and garlic, and sauté until aromatic.
Add the rice to toast for 3 minutes, stirring occasionally. Add the tomato paste you've made, stir until combined, and add the vodka to deglaze.
Separately, have the stock heating up in a separate pan, which you will use to add stock into the risotto as you stir and cook for about 30 minutes.
Taste. Season with salt and pepper. Fold in some fresh basil. Serve immediately with a heavy drizzle of olive oil.