Preheat the broiler to high. Finely mince the shallot and place in a small bowl. Cover with the lemon juice and a pinch of salt and freshly cracked pepper. (I like to add a pinch of sugar, too.) Set aside to macerate for 15 to 20 minutes. Use a fork to whisk in the olive oil. Taste and adjust seasoning as necessary.
Meanwhile, quarter the heads of endive through the core, then finely slice crosswise. Place in a large bowl. Scatter the scallions over top. Break the smoked trout into large pieces over top. Pour the dressing over top, and use your hands to gently toss everything together, keeping the trout in largish pieces. Taste and adjust seasoning as needed—now is the time to correct for seasoning because once the avocado is in, you don’t want to toss too much or it will all turn to mush.
Dice the avocado, and add to the bowl followed by the parsley. Toss with your hands again gently until combined. Set salad aside.
Arrange bread on cooling rack set on sheet pan. Drizzle lightly with olive oil. Broil 2 minutes or until lightly golden, keeping a close watch. Remove pan from oven, flip slices of bread over, drizzle with more oil, and return pan to the oven for another 2 minutes, or until bread is golden. Transfer toasts to a platter. Mound trout and avocado salad over top. Serve immediately.