Heat 1 tablespoon olive oil in a large skillet over medium-high heat.
Add the beef cubes and cook for 4-5 minutes until browned on all sides. Remove beef from skillet and set aside.
Add the remaining 1 tablespoon olive oil to the skillet.
Add the chicken pieces and cook for 5-6 minutes until browned and cooked through. Remove chicken from skillet and set aside with beef.
In the same skillet, add the diced onion and cook for 3 minutes until softened.
Add the minced garlic, sliced red and green bell peppers, and sliced carrots. Cook for 5 minutes until vegetables begin to soften.
Stir in the tomato paste and cook for 1 minute.
Pour in the beef broth and chicken broth, then add dried thyme, dried rosemary, black pepper, salt, and Worcestershire sauce. Stir to combine.
Return the cooked beef and chicken to the skillet. Bring the mixture to a simmer.
Cover and cook for 20 minutes, stirring occasionally, until the vegetables are tender and the meat is fully cooked.
In a small bowl, mix the cornstarch with cold water to create a slurry.
Slowly stir the cornstarch slurry into the skillet and cook for an additional 2-3 minutes until the sauce thickens.
Remove from heat and sprinkle with chopped fresh parsley before serving.