Combine the low-sodium chicken broth, oil-packed sun-dried tomatoes, garlic, Italian seasoning, paprika, fine salt, and ground black pepper in a 4- to 6-quart slow cooker.

Nestle the boneless skinless chicken breasts into the broth in a snug layer.

Cover and cook on LOW for about 3 hours, checking the thickest part with a thermometer; continue as needed, up to about 4 hours, until every piece reaches 165°F. Keep the lid closed except for the temperature check.

Transfer the cooked chicken to a covered plate while finishing the sauce.

Stir the heavy cream into the hot cooking liquid and switch the slow cooker to HIGH.

Whisk the cornstarch and cold water together in a small cup until smooth.

Stir the slurry into the sauce, cover, and cook on HIGH for 15 to 25 minutes, until lightly thickened; the sauce should coat a spoon rather than become a paste.

Turn off the cooker and stir in the grated hard Italian-style cheese until melted.

Return the chicken and any collected juices to the hot sauce and spoon the sauce over each piece before dividing into 6 servings.