The day before, pluck the basil leaves and cut into fine strips. Coarsely crush the fennel seeds in a mortar. Mix the basil and fennel seeds with 2 tablespoons of olive oil, salt and pepper.
Turn the goat cheese in a bowl in the basil oil, cover with cling film and leave to marinate overnight.
The next day, quarter and core the peppers and cut into 2 cm pieces. Peel and roughly chop shallots and garlic.
Heat 2 tablespoons of olive oil in a saucepan. Sauté paprika, shallots, garlic in it over medium heat for 4-5 minutes until translucent, deglaze with wine and reduce by half. Pour in the vegetable stock, simmer gently for 35 minutes over a medium heat, do not put the lid on completely.
Finely puree the soup in the pot with a cutting stick and pour through a not too fine sieve into another pot. Pour in the cream and bring to the boil briefly. Season with salt, pepper and a pinch of sugar, keep warm.
Remove the cheese from the marinade and drain well on kitchen paper.
Whisk the egg in a bowl. Turn goat cheese one after the other first in egg, then in breadcrumbs. Repeat the process, lightly pressing the breading on. Heat the rest of the olive oil in a pan. Fry the goat cheese thalers on both sides over medium heat until golden brown.
Divide the soup on 4 plates. Serve 1 goat cheese thaler in each and garnish with a little basil.