In a small bowl, whisk together the paprika, brown sugar, salt, onion powder, garlic powder, thyme, oregano, cayenne, and black pepper to create the spice blend.
Pat the chicken cutlets and shrimp dry with paper towels. Season all sides of the chicken and shrimp generously with the spice blend.
Melt 3 tablespoons of butter in a large skillet over medium-high heat. Add the seasoned chicken and cook for 3-4 minutes per side, until browned. Add the shrimp and cook for 1-2 minutes, just until they turn pink. Transfer the chicken and shrimp to a plate.
Reduce the heat to medium. Add the remaining 3 tablespoons of butter to the skillet. Once melted, add the sliced onion and mushrooms and sauté for 5-6 minutes, until softened and browned.
Add the minced garlic to the skillet and cook for 30 seconds until fragrant.
Pour in the chicken broth to deglaze the pan, scraping the bottom with a spoon to release any browned bits. Bring the sauce to a simmer.
Return the chicken and shrimp to the skillet. Let everything simmer together for 2-3 minutes, until the sauce has slightly thickened and the chicken is cooked through.
Confirm the chicken has reached an internal temperature of 165°F (74°C) and the shrimp are opaque and have reached 145°F (63°C).
Remove from heat and garnish with fresh parsley before serving.