To peel the tomatoes, you'll want to cut out the stem and cut a small X on the bottom of each tomato. Get a pot of water boiling and set a bowl of ice water nearby. Drop the tomatoes in the boiling water one at a time for about 30-60 seconds, remove and plunge into the ice water until cool. The skin should easily peel off.
Keep the water boiling while you seed and dice the tomatoes. Put the chopped tomatoes into a strainer to get rid of the excess moisture.
Heat the oil in a large, deep pan over medium heat. Add the garlic and sauté until fragrant. Remove the pan from the heat, add the vodka, and return to heat. Stir the vodka and oil until the alcohol is cooked out. If you still smell the alcohol fumes, it's not ready yet.
Once the alcohol cooks out, add the tomatoes, basil, salt and pepper. At this point, start cooking the pasta.
Simmer the tomatoes over medium-low heat for 15-20 minutes, until they are all softened. Taste and add more salt if needed.
When the pasta is done, drain it and add it back to the pot. Toss with a small amount of oil and add the tomatoes when they are done. Toss well to combine and either serve immediately or cover and let it sit for 30 minutes so the pasta can absorb the flavors.