Combine the water, brown sugar, soy sauce, salt, and pepper and stir until salt and sugar are dissolved. Brine the trout in the refrigerator for 60 minutes.
Heat grill to 225°F, and place trout directly onto grill grates, skin side down. Close the lid.
Smoke trout for 1½ – 2 hours until the fish starts to flake and turns slightly opaque in color.
Remove trout once they are fully cooked; transfer to a baking sheet.
De-bone each fish, and then serve with Dilly Walnut Pesto.
For the Dilly Walnut Pesto
In a food processor, add the walnuts and pulse until they are ground into fine crumbs.
Add parsley, garlic, parmesan, olive oil, and salt to the food processor, pulse until it’s blended.