Step 1

In a skillet, heat the 2 tablespoons of oil. Add the onion, leeks, thyme and marjoram. Season with salt and pepper. Cook over moderately low heat, stirring, until softened, 10 minutes. Add the sugar, vinegar and carrot and cook until the liquid has evaporated, 5 minutes. Transfer to a bowl and refrigerate until cool.

Step 2

Add the tuna and its oil to the vegetables, breaking the tuna into large flakes.

Step 3

Preheat the broiler. Brush the cut side of the baguettes with oil and toast slightly. Rub the cut sides of the tomato over the baguettes, leaving lots of pulp. Spoon the tuna onto the baguettes, top with the piquillos; serve.