Peel the onion. Cut peppers in half and remove seeds. Cut peppers and onion into cubes. Heat butter in a saucepan. Sauté vegetables in it. Add vegetable soup and simmer for about 15 minutes at low heat.
Pluck basil leaves, rinse and dry with kitchen paper. Peel the garlic cloves and mash them with the basil leaves, the almond kernels, the olive oil, the vinegar and the Parmesan cheese. Add the double cream and season to taste with salt and freshly ground pepper.
Bake garlic-butter baguettes. Mash soup and pour in whipped cream.
Season to taste with salt and freshly ground pepper. Divide hot soup evenly among four plates. Form pesto dabs in the center and stir gently.
Bring the soup to the table together with the bread and the remaining pesto.