Cut 2 large boneless, skinless chicken breasts in half horizontally to get 4 pieces total. Pat dry with paper towels. Season all over with 1 teaspoon kosher salt, 1 teaspoon paprika, and ½ teaspoon black pepper.
Heat 1 tablespoon olive oil in a large, 12-inch cast iron or stainless steel skillet over medium heat until shimmering. Add the chicken in a single layer and sear until browned, cooked through, and an instant-read thermometer inserted into the thickest part of the chicken registers at least 165°F, 3 to 4 minutes per side. Transfer to a large plate.
Add ¾ cup low-sodium chicken broth to the skillet and cook, scraping up all the browned bits with a wooden spoon, for 30 seconds to 1 minute. Whisk in 6 ounces cubed room-temperature cream cheese and 1 ½ teaspoons Dijon mustard until smooth, 2 to 3 minutes.
Return the chicken and any juices on the plate to the skillet. Garnish with finely chopped fresh parsley leaves if desired.
