Preheat the oven to 350˚F / 180˚C. You will need a baking dish or ovenproof skillet that is about 9 inches (23 cm) in diameter (I use a cast-iron skillet, but a rectangular baking dish works, too). Drizzle with 1–2 tablespoons of olive oil and tilt the dish or pan so the oil lightly coats the base and sides.
Place the tomatoes in a large bowl, along with the garlic, 1 teaspoon of sea salt, the thyme leaves, vinegar and sugar. Using clean hands, squeeze the tomatoes until they burst, just enough to allow some of the juices to flow out. Tip this mixture into the prepared dish or pan, and keep the bowl to use again at the next step.
Add the milk and eggs to the bowl and whisk until well combined. Add the flour, Gruyere, about 1 teaspoon of sea salt and a few turns of freshly ground black pepper. Whisk until well combined (some lumps are okay).
Pour the batter over the tomatoes and give the dish or pan a shake so it can settle among the tomatoes. Place on the middle rack of the oven and bake for 35–40 minutes, until the center is just set, with a slight wobble. Remove from the oven and allow to cool for 10–15 minutes before serving—this is important as it allows everything to meld together. Serve topped with the chives or green onion.