Put the mussels into a large bowl of ice water. Discard any that remain open when tapped, then drain well and pull away any ‘beards. (Fresh mussels look black and shiny and should only smell pleasantly of the deep sea – the vast majority should be tightly closed. Avoid any that smell ‘fishy’, look dry or are mostly open.)
Roll the chili in your hands to loosen the seeds, then slit in half and shake out the seeds. Slice the flesh into thin sticks, then stack together and finely chop. Pick over the thyme sprigs, discarding the thick stalks, and pick the parsley leaves from the stalks. Prepare the pommes frites.
Heat the butter and oil in Dutch oven or heavy-based sauté pan (with a lid) on the stove on low heat.
Add the minced shallots, garlic and chili. Stirring frequently, cook until translucent and soft.
Add the white wine and Pernod and bring to a boil to reduce the wine by half. Add the thyme and season with salt and pepper.
Gently add the mussels to the cooking broth, cover with lid and steam for approximately 5-7 minutes, stirring occasionally until mussels open. Using a slotted spoon, divide the mussels evenly into four serving bowl, discarding any that remain closed.
While the mussels are steaming bring the pot of oil back to 375° so you can second-fry the potatoes as soon as you have removed the mussels. This time until they are a dark golden brown. Remove with the slotted spoon back onto the rack, lightly salt and toss with the fresh parsley.
Add the crème fraiche, chives and whole parsley leaves to the remaining cooking liquid and bring just to a boil while stirring to combine. Pour the sauce over mussels, garner with some of the fresh chopped parsley and serve with the pommes frites and mayonnaise.