Heat the olive oil in a large pot over medium heat. Add the onion and cook until softened, about 5 minutes. Stir in the garlic and cook for 1 minute more.
Pour in the white wine and add the thyme sprigs. Simmer until the wine reduces by half, roughly 4 minutes.
Add the diced tomatoes, fish broth, and Kalamata olives. Season with a pinch of salt and pepper. Bring the mixture to a gentle simmer and cook for 10 minutes to let the flavors blend.
Add the branzino pieces to the pot. Cover and cook for 6 to 8 minutes until the fish turns opaque and flakes easily.
Remove the thyme sprigs. Taste and adjust salt and pepper if needed. Ladle the stew into bowls and finish with chopped parsley and a squeeze of lemon.