Boil a large pot of salted water and cook the rigatoni according to the package directions.
Drain and rinse with cold water to stop the cooking process and cool it down for the salad.
Make the dressing by whisking together the grated garlic, balsamic vinegar, and olive oil until emulsified. Season with salt and pepper to taste.
In a large bowl, combine the cooked pasta, tomato confit, chopped shallot, and half of the basil and chives.
Pour the balsamic dressing over the pasta salad and toss to coat evenly.
Gently tear the burrata into pieces and add to the salad along with the remaining basil leaves and chives.
Sprinkle the chopped pistachios on top and serve!