In the bowl of a food processor, combine the sun-dried tomatoes and their oil, garlic, basil, red pepper flakes, and nuts. Blend until roughly combine. Add the parmesan cheese and while continuously blending add the remaining 1/4 c. olive oil in a slow steady stream until the mixture comes together. (it will be thick) Check seasonings and add salt and pepper only if needed. Set aside or refrigerate until needed. Bring up to room temp. before using.
Cook the pasta in a large pot of boiling salted water until tender but still firm to the bite, stirring occasionally, about 8-15 minutes or as directed on the package. Drain, reserving 2 cups of the cooking liquid.
In the same warm pot you used to cook the pasta in add the pesto to the pasta and toss to coat, adding enough reserved cooking liquid to moisten and bring it together. Add the shredded chicken and mix well.
Transfer to a serving dish. Serve sprinkled with a little extra parmesan!