Fill a large pot with water and place over medium-high heat on the stove. Bring the water to a boil. Add salt generously. Add pasta and cook for 1 minute less than the package directions. Reserve 1 cup of pasta water in case you want to add it to the dish later. Set that aside.
While the pasta noodles are cooking you can toss your sun-dried tomatoes, the oil from the sun-dried tomatoes, the garlic, salt, white pepper, sweet basil, half of the parmesan cheese, and walnuts in a food processor. Pulse until smooth. If the mixture is still too thick add a touch of olive oil to start and pulse while adding the oil until you get the desired consistency you like. It's always best to start with a little, you can always add more but you can't take away. So go easy initially and add oil to taste if needed.
Transfer pesto to a large skillet or non-stick pan and heat on medium heat just before adding the cooked noodles. Then use a slotted spoon to lift out the noodles and transfer them to the large skillet or non-stick pan. Do not rinse the noodles.
Toss the pasta together in the skillet or non-stick pan. Start by adding about ¼ cup of the reserved pasta water and then toss the pasta again. If you need more pasta water to thicken the pasta you can add until you get the desired thickness you like. I added almost all of it to mine to thicken it.