Boil a large pot of water for the fettuccine. Salt the water with 1 heaping Tablespoon Kosher salt. Once boiling, cook to al dente, then drain and toss with olive oil so it doesn't stick together.

Heat 1 Tablespoon of the oil in a large, deep skillet over medium heat. Season the chicken breasts with salt and pepper on both sides, then place in the skillet. Cook undisturbed for 4-5 minutes, then flip, cooking an additional 3-4 minutes, or until internal temperature registers 165 degrees.

Remove the chicken from the skillet and tent with foil to keep warm. Add the rest of the olive oil to the pan followed by the shallots. Saute 1-2 minutes until starting to soften. Add the garlic and sun dried tomatoes, and saute for another 1-2 minutes, until shallots are softened.

Deglaze the pan with the white wine, scraping up any browned bits at the bottom of the pan.

Stir in the half and half and cream and bring to a gentle simmer, then lower heat to medium low to maintain the simmer. Cook for 2-3 minutes, stirring often, until sauce is slightly thickened. Stir in the Parmesan cheese until melted. Remove from heat and stir in basil leaves, stirring until wilted.

Serve the sauce tossed with the pasta and sliced chicken breast.