Step 1Heat oven to 400 degrees. In a large bowl, whisk together the milk, Parmesan, quarter-cup Gruyère, 2 tablespoons of the mixed herbs, the butter, salt and eggs. Add the flour and whisk until just combined (the batter will be lumpy; that’s OK).
Step 2Pour the batter into a 10-inch round baking dish or pie pan. Sprinkle the tomatoes evenly in the batter, then sprinkle the remaining quarter-cup Gruyère over the top.
Step 3Bake until the clafoutis is just barely set in the center and the edges are golden brown, 15 minutes. Remove the dish from the oven, arrange a rack just below the broiler, and heat the broiler to high. Place the dish under the broiler and cook until the cheese on top is golden in spots, 1 1/2 to 2 minutes.
Step 4Transfer the skillet or dish to a rack and let cool for 5 minutes. Sprinkle the remaining 1 tablespoon minced herbs and a pinch of flaky sea salt over the clafoutis to serve. Cut it into wedges or scoop it into bowls and serve with more Parmesan.