In a small bowl, whisk together the mayonnaise, olive oil, mustard, capers, lemon juice, garlic, turmeric, salt, and several grinds of black pepper.
Mix in the tofu and then lightly crumble it with your hands, keeping some of the cubes intact. We're going for the texture of egg salad, not scrambled eggs.
Stir in the celery seed, dill, and chives. Chill until ready to serve.
Assemble the sandwiches with watercress or spring greens, a scoop of the egg salad, and pickled onions and radish slices, if desired.