Halve the cherry tomatoes and chop them to about the size of a pea. Put them in a fine-mesh sieve over a bowl, toss with 1/2 tsp of the salt, and let them drain for 10 minutes, pressing gently with a spoon once or twice. Chop the onion, mint and parsley while you wait.
Tip the drained tomatoes into a 3-quart / 2.8 L mixing bowl. Add the onion, mint, parsley, oregano, pepper and the remaining 1/2 tsp salt, then stir in the flour and baking powder until no dry streaks remain. The batter should be thick and drop off the spoon in clumps. If it runs, stir in 1 tbsp more flour at a time.
Pour 120 ml of olive oil into a 26 cm / 10-inch heavy skillet and heat over medium heat for 2 to 3 minutes, until the oil reaches 175 C / 350 F or a bit of batter sizzles right away.
Drop heaping tablespoons of batter into the oil, about 2 tablespoons per fritter and 5 or 6 per batch. Flatten each one lightly to about 1.5 cm / 1/2 inch thick and leave 2 cm between them. Fry for 2 to 3 minutes per side, until deep golden and crisp at the edges and firm when pressed in the middle. Lower the heat a little if they brown in under 2 minutes.
Move the fritters to a wire rack set over a 33 x 46 cm / 13 x 18-inch sheet pan. Add 1 to 2 tbsp oil to the skillet between batches and wait 30 seconds for it to heat up. Repeat with the remaining batter for 3 batches, about 16 fritters in total, and serve within 20 minutes.