Baccala Fritto: Fried Salt Cod

Name: Baccala Fritto: Fried Salt Cod
Ingredients: 2 pounds salt cod, portioned into 8-ounce fillets, all bones removed; 1 cup semolina flour; 1 cup all-purpose flour; 1 tablespoon baking powder; 1 tablespoon baking soda; 2 tablespoons plus 2 tablespoons extra-virgin olive oil; 2 quarts olive oil, for frying; 1 cup coarse bread crumbs; 1 cup parsley leaves, loosely packed; 1 small red onion, thinly sliced; 1 pint cherry tomatoes, stems removed and cut in half; 1 tablespoon freshly-squeezed lemon juice; Salt and pepper, to taste