Smoked Trout Lettuce Wraps with Meyer Lemon Dressing and Carrots

Name: Smoked Trout Lettuce Wraps with Meyer Lemon Dressing and Carrots
Ingredients: 1/2 cup kosher salt; 2 tablespoons light brown sugar; 8 rainbow trout fillets; 1/4 cup freshly squeezed Meyer lemon juice; 2 tablespoons mayonnaise; 1 heaping tablespoon whole grain mustard; 1 tablespoon red wine vinegar; 2 teaspoons honey; 1/2 teaspoon finely grated lemon zest; Kosher salt and freshly ground pepper; 1/2 cup extra-virgin olive oil; 1 head butter lettuce, leaves separated; 1 carrot, julienned or grated; 1 cup fresh parsley leaves