Rinse the mussels under cold water, scrubbing the shells and removing any beards. Discard any open or cracked mussels that do not close when tapped. This ensures only the freshest mussels make it to the pot.
Peel the potatoes and cut them into uniform fries. Soak them in cold water for at least 30 minutes to remove excess starch, resulting in crispier fries.
Heat the vegetable oil in a deep fryer or heavy bottomed pot to 140°C (285°F). Drain and pat the potatoes dry with a kitchen towel. Fry them in batches for 4-5 minutes until pale and slightly softened. Remove with a slotted spoon and let them rest on a wire rack.
In a large pot or Dutch oven, melt the butter over medium heat. Sauté the shallots and garlic until fragrant and translucent, about 2 minutes. Stir frequently to prevent burning.
Pour in the white wine and fish broth, then add the bay leaf and thyme. Bring the liquid to a gentle simmer. The wine adds depth, while the herbs infuse the broth with aromatic flavours.
Increase the heat to high and add the cleaned mussels. Cover with a tight fitting lid and steam for 5-7 minutes, shaking the pot occasionally. The mussels are ready when they open. Discard any that remain closed.
While the mussels cook, increase the oil temperature to 180°C (350°F). Fry the pre-cooked fries in batches for another 2-3 minutes, until golden and crisp. Drain on paper towels and sprinkle with sea salt.
Remove the mussels from the heat. Discard the bay leaf and thyme sprigs, then stir in freshly chopped parsley. Ladle the mussels and broth into serving bowls.
Serve the mussels immediately with a side of crispy fries and lemon wedges. Traditionally, moules frites is accompanied by mayonnaise or aioli for dipping.
Pair this dish with a chilled Belgian beer or a crisp white wine. Serve in deep bowls with an extra empty dish for discarded shells. Encourage diners to enjoy the broth by sipping or soaking it up with bread.