Heat the oil in a sauté pan over medium heat. Add beef and cook until golden brown.
Melt butter in a saucepan over medium heat. Add garlic, peppers, onion, celery, and cook, stirring frequently, until soft, about 3-5 minutes. Then add the flour and remaining Cajun seasoning. Cook until the flour turns deep golden brown.
In a large pot of boiling salted water, cook pasta according to package instructions; drain well.
Gradually stir in the broth, tomatoes, thyme, and lemon zest. Cover with a lid and bring to a simmer for 10 minutes. Remove the lid and add the chicken to the pan. Simmer until the chicken reaches an internal temperature of 160°F using a thermometer.
Toss the pasta in the sauce and serve immediately so the pasta doesnt soak up all the sauce. Garnish with parsely.