Heat 6 quarts of water in a large pot on high heat. When the water is boiling, add 1 tablespoon of salt and two tablespoons of olive oil. Reduce heat to simmer and add pasta. Cook, stirring occasionally, according to directions until barely al dente. (Just barely done.)
While the pasta is cooking:
Drain sun-dried tomatoes. (Put the oil back in the jar to use later!) Chop the sun-dried tomatoes into 1/4"-1/2" pieces. Set aside.
In a medium bowl, whisk together eggs, milk, and half of the Parmesan.
When the pasta is done, drain it thoroughly in a colander, reserving 2 cups of the cooking liquid.
Heat a Dutch Oven or other heavy bottom pot over medium-high heat. Add 1 cup of the reserve pasta cooking liquid and bring to a boil.
Reduce heat to medium. Add drained pasta pasta to hot cooking liquid in Dutch oven and stir constantly, using tongs, until most of the liquid is absorbed.
Whisk 1/2 cup reserve cooking liquid into egg mixture. (This tempers the egg mixture. DO NOT skip this step!)
Slowly drizzle the egg mixture into the hot pasta, tossing it all constantly with tongs as you do. Continue stirring with tongs until egg mixture thickens to make a creamy sauce. Remove carbonara from from heat. I usually remove the pot from the heat when the sauce is just beginning to come together, and let it continue cooking in the residual heat. The trick is to keep the sauce constantly moving until it has thickened. NOTE: If the sauce is too thick, you can use some of the remaining reserve liquid to thin it. Add about 1-2 tablespoons at a time, until the sauce is the consistency of heavy cream. (You will probably not use all of the reserve liquid.)
Once the sauce is as you like it, toss in half of the chopped sun-dried tomatoes, half of the basil, and half the Parmesan. Mix with tongs.
Finish with freshly ground pepper, and the remaining parmesan, sun-dried tomatoes, and fresh basil.
Angel Hair Pasta: You can use fettuccine or spaghetti, but angel hair is our favorite, plus it cooks in no time!
Sun-dried Tomatoes: 1 cup of drained, chopped, oil-packed sun-dried tomatoes weighs about 5 ounces.
Milk: For a richer sauce, use half-and-half or cream.
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