Heat the oven to 425°F. Place a rimmed baking sheet inside to preheat.
Toss peppers and onion with the vinegar and 0.5 teaspoon salt. Let sit 10 minutes to soften.
Whisk the flour, cornmeal, Parmesan, remaining salt, black pepper, red pepper flakes, and thyme in a bowl.
Pour in the water and 2 tablespoons olive oil. Whisk until you have a thin, smooth batter.
Fold the marinated peppers and onion into the batter, coating them evenly.
Carefully remove the hot pan. Brush it with the remaining 1 tablespoon olive oil.
Spread the mixture onto the hot pan in a very thin, even layer.
Bake 25–30 minutes until the edges are deep golden and crisp.
Broil 1–2 minutes for extra color if needed. Cool 5 minutes, then slice and serve.