How to Make It
In a saucepan, toast the coriander seeds over low heat until fragrant. Add the vinegar, sugar, salt and 1/4 cup of water and cook, stirring, until the sugar dissolves and the brine is warm. Stir in the carrot slices and let stand for 1 hour.
Drain the carrot, reserving the pickling liquid. Transfer the carrot and 1 tablespoon of the pickling liquid to a blender. Add the butter and cilantro and puree. Pass the butter through a fine sieve into a bowl and season with salt.
In a saucepan, bring 1 inch of water to a boil. Add the mussels, cover and cook just until they open. Drain and remove the mussels from their shells. In a bowl, toss the mussels with the olive oil and chives.
Spread some of the carrot butter on the toasts. Top with the mussels, drape the lardo on top and serve.