Heat oven to 400 degrees. Pull 1 tablespoon thyme leaves off the bunchand finely chop.
Season fish all over with a large pinch or two of salt and pepper and rub with chopped thyme leaves. Let rest at room temperature while you prepare peppers.
Spread peppers on a rimmed sheet pan, and toss with 1 1/2 tablespoons oil, 1/2 teaspoon salt and the black pepper to taste. Top peppers with the remaining thyme sprigs. Roast, tossing occasionally, until peppers are softened and golden at the edges, 15 to 20 minutes.
Increase oven temperature to 500 degrees. Push peppers to the edges of the pan, clearing a space in the center. Lay fish out on that empty space and drizzle with oil. Scatter olives over the top of fish and peppers. Roast until fish turns opaque and is just cooked through, 6 to 10 minutes.
Meanwhile, make a vinaigrette by combining vinegar, garlic and a pinch of salt in a bowl. Whisk in remaining 3 tablespoons olive oil, then whisk in parsley. Taste and add more salt or vinegar, or both, if needed. Serve fish and peppers drizzled with vinaigrette.
