Clean the mussels by removing the beards and soaking the mussels in clean water. Drain the water and set the mussels aside until needed.
Heat the oil in a large cast iron potije pot over medium coals, cook the onions and the thyme leaves in a little oil until the onions are soft and translucent.
Add white wine and cook over medium heat until the liquid is reduced by half and the alcohol has evaporated.
Add the fresh cream and cook over low heat, another 20 minutes. Stir in the garlic and butter. Season to taste and remove from heat.
Steam the mussels in a pot of salted water, covered by a lid, until the shells open. Discard any unopened mussels.
Add the mussels to the sauce, garnish with fresh parsley, and serve with toasted bread and lime wedges for squeezing.