Wash the zucchini and cut into fine slices. Blanche for 1-2 minutes in boiling, salted water, drain, and run under cold water.
Cut the eggplant into small cubes. Place in a pan with 2 tablespoons olive oil and salt. Cover and cook or 8 minutes, then puree the eggplant and add the Piment d’Espelette.
Separately, place the goats’ cheese, lemon juice, chopped chives and basil, 2 tbsp olive oil and Piment d’Espelette and salt in a processor. Puree the cheese mixture.
Cut the sweet red peppers into small cubes and fold into the cheese mixture.
Line a small soufflé dish, chosen to contain the ingredients you are working with, with the slices of zucchini. Layer the cheese puree to fill ⅓ of the dish, add the eggplant puree in a layer, and finally, layer the remaining cheese puree.
In the processor, mix the garlic, lemon juice, remaining olive oil, salt and Piment d’Espelette to make vinaigrette. Turn out the goats’ cheese cake onto a plate and drizzle with the vinaigrette.