In a large saute pan, combine the mussels, onion, parsley, wine, thyme, bay leaf, black pepper, to taste, saffron, and olive oil and bring to a boil over high heat. Continue cooking, shaking the pan occasionally, until the mussels have all opened. Remove from heat and remove the mussels with tongs, to a large bowl. Set aside. Reserve the cooking liquid.
Once the mussels are cool enough to handle, remove 1 half of each shell and discard. Place the half-shelled mussels in the refrigerator to chill, and reserve the juices from the bowl. Strain this liquid, as well as the liquid from the saute pan, and combine in the saute pan. Reduce by 2/3 over high heat, then remove from heat, and set aside to cool. Once it is cooled, drizzle over the chilled mussels and serve.