Arrange the peppers and tomatoes on the large baking sheet. Transfer the baking sheet to the oven and roast for 30 minutes.
Roll the goat cheese into a series of small balls. Arrange the goat cheese on a plate and transfer it to the freezer. Freeze for 30 minutes.
Once the oil is simmering, add the onions, carrot, and celery along with a generous pinch of salt. Sauté the veg until the onions are translucent.
Pour in the stock and add the roasted vegetables. Bring the soup up to a boil and reduce it to a simmer. Add the bay leaves and thyme and simmer for 15-20 minutes.
Roll the goat cheese first in the cornstarch, then the egg, and finally the panko breadcrumbs. Fry the goat cheese is golden on all sides.
Take the soup off of the heat and using a food processor or immersion blender, puree until smooth. Stir in the cream.