Prepare the brine: Combine the water, salt, sugar, bay leaves, peppercorns, coriander, allspice, and mustard in a pot. Bring to a simmer, stirring until the salt and sugar are dissolved.
Cool, then chill the brine.
Place the trout fillets in a stainless-steel, plastic, or other nonreactive pan in a single layer. Add enough cold bri