Heat a medium saucepan over a medium heat and add a lug of olive oil. Sweat the shallots down slowly until soft and then add the chestnuts. Season well, pour over the stock and bring to the boil.
Turn down to a simmer and cook for about 10 minutes to soften the chestnuts and reduce the stock. Once reduced, remove from the heat and add the cream. Stir well.
Blend the soup in a processor adding the liquid a bit at a time. You want a fairly thick, soupy consistency. Season to taste and keep warm.
For the Migas, fry the breadcrumbs with the garlic and thyme over a medium heat in plenty olive oil. The crumbs should be golden brown. Season to taste and drain well.
Divide the soup between bowls and the sprinkle over the Migas and serve with some extra thyme and olive oil.