Heat the oil in a large skillet over medium heat, and sauté the onion, garlic, celery, and bell peppers until soft and fragrant, about 4-5 minutes.
Add the tomatoes, Anaheim chili, herbs, spices, salt, and pepper, and cook until the tomatoes are soft, about 5 more minutes.
Pour in the chicken broth and cornstarch slurry. Bring to a boil, reduce the heat to medium-low, and simmer for 10-12 minutes to let the flavors develop and the sauce thicken.
Mix in the shrimp and cook for 2-3 minutes, just until they change color from grey to pink. Don't overcook them or they will turn out rubbery and tough. Sprinkle chopped parsley on top.
Serve over freshly cooked rice and lime wedges on the side.