In a large stockpot, heat olive oil over medium heat. Add garlic and half of the parsley, reserving the remainder for garnish.
Mix in tomatoes, anchovies, vegetable broth, salt, pepper, and red chili flakes. Increase heat to high and bring the pot to a boil. Reduce heat to medium-low, cover the pot, and simmer for 20 minutes.
Remove lid and add halibut. Replace cover and cook for an additional 8 to 10 minutes, or until fish easily flakes apart.
Remove from heat and break down halibut into small pieces. Mix to evenly distribute the fish and serve garnished with the remaining fresh parsley.