Combine the basil in with the walnuts, pulse a few times in a food processor. Add the garlic, salt and pepper then pulse a few times more.
Slowly add the olive oil in a constant stream while the food processor is on. Stop to scrape down the sides of the food processor with a rubber spatula. Add the grated cheese and pulse again until blended.
If the chicken is frozen, then cook the chicken in about a half cup of water till it is thawed enough to dice into cubes. Smash the garlic and add to the water and finish cooking the chicken.
Boil a pot of water and add the egg noodles and cook to desired softness, I like mine a little al dente so it only took about 6 minutes. Drain the water from the noodles and chicken and mix it all together with the pesto.