Pecan butter: Place all pecan butter ingredients into the container of a food processor or blender. Cover and process to a smooth puree. Set aside.
Sauce: In a small bowl, combine flour and 2 Tbs. water to make a smooth paste. In a small saucepan, bring stock, Worcestershire sauce, and lemon juice to a light boil.
Whisk about 1/3 cup of the hot stock mixture into the flour paste. Then gradually pour the flour mixture back into the saucepan, stirring constantly with the whisk, and bring to a boil. Whisk in the softened butter, a tablespoon at a time. Keep sauce warm.
To prepare the fish, blend the Creole seasoning and salt into the flour in a wide bowl. Beat the eggs with the milk in a second wide bowl.
Dust the trout lightly with the seasoned flour. Pass it through the egg wash, and then dredge it through the seasoned flour.
In a large skillet, heat half of the clarified butter over medium-high heat until a sprinkling of flour sizzles in it. Add three fillets of trout and sate three or four minutes, until golden brown, turning once. Transfer fillets to serving platter and keep warm. Add the rest of the butter to the pan and sate the remaining trout.
Spread pecan butter over trout, sprinkle with roasted pecans, and top with the sauce.