Heat olive oil in a large pan over medium-high heat. Add chicken & grind fresh pepper on each side. Cover & cook until done, about 5 minutes on each side. (When done, chicken will have NO pink on the inside.) Remove from heat and set aside, keeping covered.
In a large saucepan, melt butter over medium heat. Add onion, garlic, & shallots, cooking 1-2 minutes, just until soft. Add sun dried tomatoes; stir. With a whisk in hand, add flour & stir. Slowly pour in chicken broth, whisking constantly to remove any lumps. Add cream, still whisking. Whisk that sucker to death! (just kidding). Continue whisking for 3-4 minutes or until sauce begins to thicken. Take off heat and let sit; it will continue to thicken, feel free to stir every so often as you cook the spaghetti:
Cook spaghetti according to package directions. It is done when it is soft, but still has a bite; al dente please.
Add fresh basil to sun dried tomato sauce and give it a good stir.
Place spaghetti noodles on serving plates, placing chicken directly on top of noodles. Spoon as much sauce as you would like over chicken & noodles; enjoy!