Add the mussels to a large bowl with cold water. Taking one at a time, scrub them well all over with a clean scrubbing brush, strip away any beard and place them in a colander. Repeat the process with each one and make sure they are all sealed tightly. Should any mussel be open, tap it on a surface twice; if it doesn't close, discard it. Rinse all the mussels well one more time when you have them all prepped and set them aside.
In a large pot, add the oil along with the garlic, chiles and shallots. Turn the heat to medium and saute until they become fragrant and the shallots become translucent, about 4 minutes.
Add the cleaned mussels and stir them around with the shallot mixture. Pour over the beer, cover the pot and bring to a boil. Cook until all of the mussels have opened, 5 to 7 minutes.
Remove from the heat, then add the cream and parsley and stir to incorporate. Plate the mussels in a large serving bowl surrounded by the grilled bread.