Season the bite-sized chicken pieces with salt and pepper.
Heat the olive oil in a large nonstick skillet over medium-high heat, then add the chicken and cook for about 2 minutes to brown the pieces.
Add the minced garlic to the skillet and cook for about 1 minute, stirring, until fragrant.
Stir in the half-and-half, pesto, and crushed red pepper flakes until combined and bring the mixture to a gentle simmer.
Submerge the refrigerated tortellini in the simmering sauce as much as possible, then reduce the heat to maintain a gentle simmer (do not boil) to avoid curdling.
Cover the skillet and cook for 4 to 5 minutes, or until the tortellini are tender and cooked through; if you don't have a lid, cover with a round baking sheet or foil.
Remove the skillet from the heat and stir in the slivered sun-dried tomatoes and shredded Parmesan until the cheese melts into the sauce.
Taste and adjust seasoning with salt and black pepper as needed, then sprinkle with chopped parsley and serve.