How to Make It
In a medium bowl, beat the eggs with the milk, flour, 2 tablespoons of the mustard, 1 tablespoon of the oil and a generous pinch of salt. Let the batter stand for 15 minutes.
Preheat the oven to 400°. Set a steamer basket in a medium saucepan filled with 1 inch of water. Add the carrots, cover and steam over high heat until just tender, about 4 minutes.
Add the remaining 2 tablespoons of oil to a 9-inch-square baking pan and heat in the oven for 10 minutes.
Meanwhile, in a large skillet, melt the butter. Add the onion, garlic and a generous pinch of salt and cook over moderately high heat, stirring, until the onion just starts to soften, about 3 minutes. Add the haricots verts and cook, stirring, until the onion is lightly browned and the beans are just softened, 3 to 4 minutes. Add the carrots, tomatoes, basil, thyme, rosemary and the remaining 1 teaspoon of mustard and cook, stirring, until hot, about 1 minute. Season the vegetables with salt and pepper.
Pour the batter evenly into the hot pan and scatter the vegetable mixture on top. Bake for 30 to 35 minutes, until puffed and lightly browned. Cut into squares and serve.