Scrub the mussel shells under cold running water. Pull off any fibrous beards by tugging firmly toward the hinge end. Discard any mussels with cracked shells or that stay open when tapped.

Set the cleaned mussels aside in a colander while you build the broth.

Heat the coconut oil in a wide 6-quart pot over medium heat. Add the shallots and cook for 3 to 4 minutes, stirring often, until softened and just starting to color.

Add the garlic, ginger, and lemongrass pieces. Stir for 1 minute until fragrant.

Add the red curry paste and stir it into the shallot mixture. Cook for 2 full minutes, pressing the paste against the bottom of the pot, until it darkens slightly and smells toasted.

Pour in the coconut milk and stock. Stir to combine and bring to a gentle simmer over medium-high heat.

Stir in the fish sauce and brown sugar. Taste the broth and adjust seasoning - it should be savory, slightly sweet, and aromatic. Remove the lemongrass pieces with tongs if you prefer.

Increase heat to bring the broth to a rolling simmer. Add all the mussels in one go and cover the pot immediately with a tight-fitting lid.

Steam for 4 to 6 minutes, shaking the pot once halfway through. The mussels are ready when the shells have opened wide.

Discard any mussels that have not opened after 7 minutes - do not force them open.

Remove the pot from heat. Squeeze the lime juice directly over the mussels and stir gently.

Ladle into deep bowls, making sure each serving gets plenty of broth. Top with fresh cilantro and sliced red chili. Serve immediately with lime wedges and crusty bread or steamed rice.