In a large skillet, heat olive oil, add scallions and cook for about 2 minutes. Add peas, season with salt and pepper, and cook for 2 minutes. Remove from the heat to cool while you prep other ingredients.
In a mixing bowl, make the dressing. Whisk together the mustard, mayonnaise, 1/2 cup of the lemon vinaigrette, capers, basil, preserved lemon and, if using, hot sauce. Season with salt and pepper.
Trim and cut the celery root into julienned matchsticks. A fast way of doing this: slice the root into large, thin slices using a mandolin slicer, then stack the slices and cut them into strips (or you can use the Mandoline Julienne attachment). Or just use a hand knife and cut it by hand. Your call.
Mix the julienned celery root with the celery, parsley leaves, lemon zest and smoked trout. Add the cooled peas and mix in the dressing. Season the lettuce with salt and pepper, and toss with the remaining 1/4 cup of lemon dressing. Serve the remoulade over the butterhead salad.