Bring a large pot of salted water to a rolling boil and cook the pasta according to package directions; reserve 1 cup of the pasta cooking water, then drain and set the pasta aside.
Heat the olive oil in a large skillet over medium heat. Add the minced garlic, dried basil, and red pepper flakes and sauté about 30–60 seconds until fragrant.
Add the drained, roughly chopped sun-dried tomatoes to the skillet and sauté with the garlic mixture for about 1 minute, then transfer the tomatoes to a plate and set aside.
Season the chicken pieces with the salt and sweet paprika, increase the skillet heat to medium-high, then add the chicken and cook 3–5 minutes, stirring or tossing, until the pieces are cooked through and lightly browned.
Return the sun-dried tomatoes to the skillet with the cooked chicken.
Pour in the heavy cream and add the shredded mozzarella; stir over medium heat until the mixture comes to a gentle boil, then reduce to a simmer and cook, stirring constantly, until the cheese melts and the sauce is smooth. Taste and adjust salt if needed.
Add the drained pasta to the skillet and toss to combine; if the sauce is too thick, add the reserved pasta water a little at a time until you reach the desired consistency.
Serve immediately, garnished with fresh basil if desired.