Bring a large pot of salted water to a boil and cook the spaghetti until al dente, following package instructions.
Meanwhile, heat olive oil in a large skillet over medium-high heat until shimmering. Add sliced chicken breasts and cook until golden brown on both sides, about 4-5 minutes per side. Remove chicken from skillet and set aside.
Add minced garlic and chopped sun-dried tomatoes to the same skillet. Sauté until fragrant, about 1 minute, until garlic turns golden and sun-dried tomatoes release their aroma.
Pour in the heavy cream, stirring to combine with the garlic and sun-dried tomatoes. Bring to a gentle simmer and cook until the sauce thickens slightly, about 3-4 minutes. Season with salt and pepper to taste.
Return the cooked chicken to the skillet, stirring to coat with the sauce. Drain the pasta and add it to the skillet, tossing everything together until evenly coated and heated through.
Serve immediately, garnished with grated Parmesan cheese and an extra crack of black pepper if desired. Observe the sauce cling to the pasta, with bright red sun-dried tomatoes and crispy-browned chicken on top.