Chop the 4 pickled peppers and drain them well. In a bowl, combine the goat cheese, 30 fresh basil leaves (finely chopped), and the drained peppers. Season with pepper and mix well.
Cut a horizontal pocket into the thickest side of each chicken breast. Stuff with the cheese mixture, then seal each pocket with toothpicks. Season the outside of the breasts with salt and pepper.
Heat olive oil in a large pan with a lid over medium-high heat. Fry the chicken breasts 3-4 minutes per side until golden brown.
Pour the white wine and brandy into the pan to deglaze. Add the black olives, cover, and simmer on low heat for 15 minutes, turning the breasts halfway through (after 10 minutes).
Remove the chicken from the pan onto a serving plate. Pour the pan sauce with olives over the breasts. Verify the internal temperature has reached 74°C (165°F). Serve immediately.