Bring a large pot of salted water to a boil. Add the 8 oz of pasta and cook according to package instructions until al dente. Drain the pasta, reserving 1/2 cup of the pasta water.
Season the 1 lb of chicken breasts evenly with 1 tsp salt and 1/2 tsp black pepper. Heat the 1 tbsp olive oil in a large skillet over medium-high heat.
Pan-cook the chicken in the skillet for 6 to 8 minutes per side, until browned and cooked through (internal temperature of 165°F). Remove the chicken from the skillet, let it rest for 5 minutes, then slice into strips.
In the same skillet, reduce the heat to medium and melt the 2 tbsp butter. Add the 4 cloves of minced garlic and sauté for 1 minute until fragrant.
Pour in the 1/2 cup of chicken broth to deglaze the pan, scraping up any browned bits. Stir in the 1 cup of heavy cream and simmer for 3 to 4 minutes until the liquid begins to thicken.
Turn the heat to low and gradually whisk in the 1 cup of grated Parmesan cheese until melted and smooth. Stir in the 1/3 cup of chopped sun-dried tomatoes.
Add the cooked pasta and sliced grilled chicken back into the skillet. Toss everything together, adding a splash of reserved pasta water if the creamy white sauce is too thick.
Garnish with the 2 tbsp of fresh chopped parsley and serve immediately.