Meanwhile, fill a large saucepan with 3 inches (8 cm) water and the vinegar; bring to a simmer. Crack each egg into a custard cup or small ramekin. Working in two batches, gently slide eggs into water and cook until whites are set and yolks are runny, about 3 to 5 minutes. Using slotted spoon, transfer to plate.
Combine egg yolks, lemon juice, 2 tsp hot water, the salt and cayenne (if using) into a food processor. Melt butter in small saucepan over high heat, swirling constantly, until hot; immediately transfer to the food processor, and mix until thick, about 1 to 2 minutes.
Place a generous portion of smoked trout on each side of the toasted english muffin. Add a poached egg on top of the trout. Top with hollandaise sauce, chives, black pepper and cayenne.