In a small bowl, combine the sweet paprika, salt, and black pepper.
Place the four chicken cutlets on a plate and evenly season both sides with the spice blend.
Heat a 12-inch heavy-duty skillet over medium-high heat and add the olive oil.
When the oil is hot, add the seasoned chicken cutlets without overcrowding the pan and cook undisturbed 5–6 minutes until golden and browned on the bottom.
Flip the cutlets and cook 4–6 more minutes until an instant-read thermometer inserted into the thickest part reads 165°F (74°C).
Transfer the cooked chicken to a plate and loosely cover with foil to rest while you make the sauce.
Reduce the skillet heat to medium-low and add the minced garlic, chopped thyme, and chopped rosemary to the remaining oil; cook, stirring, 1–2 minutes until fragrant.
Pour in the chicken broth and simmer the mixture about 5 minutes, until the liquid has reduced by roughly half.
Whisk in the unsalted butter until melted and the sauce is glossy, then remove the skillet from the heat.
Return the rested chicken to the skillet and spoon the herb butter sauce over the cutlets to coat.
Slice each cutlet if desired, transfer to a serving plate, spoon any remaining sauce over the chicken, and garnish with additional thyme if you like.