Set the oven to 425°F (220°C). Cover a large rimmed baking sheet with aluminum foil or parchment paper rated for this temperature. Use paper towels to pat the chicken breasts dry, then place them in a large bowl. Leave the breasts whole without pounding.
Add the Cajun seasoning, sweet paprika, salt, and black pepper to a small bowl. Stir until the spices are thoroughly mixed.
Pour 1 tablespoon of olive oil over the chicken breasts and turn them to coat. Add the seasoning mixture and use your hands to distribute it evenly over the entire surface of each breast, including the sides.
Transfer the seasoned chicken breasts to the prepared baking sheet in a single layer. Leave a little space between the pieces so they are not touching or overlapping.
Place the baking sheet in the preheated oven and bake, uncovered, for approximately 20-25 minutes, or until the thickest part of each chicken breast registers 165°F (74°C) on an instant-read thermometer. Begin checking around 18-20 minutes. If some breasts finish before others, remove them individually and allow the remaining chicken to continue cooking.
Transfer the chicken from the oven and allow it to rest for 5 minutes before cutting. If desired, combine the chopped parsley with a little additional olive oil and a pinch of salt, then brush over the chicken. Serve whole or sliced.