Begin by pressing the extra-firm tofu to remove excess moisture. Wrap it in a clean kitchen towel and place a heavy object on top for about 15 minutes.
Once pressed, crumble the tofu into a mixing bowl using a fork. Aim for a consistency similar to that of mashed hard-boiled eggs.
Add the vegan mayonnaise, extra-virgin olive oil, Dijon mustard, capers, lemon juice, minced garlic, turmeric, sea salt, and freshly ground black pepper to the crumbled tofu. Mix well until everything is evenly combined.
Stir in the celery seed, chopped dill, and chives. Taste and adjust seasoning if necessary.
Lay out the whole-grain sandwich bread slices. If desired, add a layer of watercress or spring greens to each slice. Spoon a generous amount of the vegan egg salad onto one slice, then top with pickled red onion and radish slices, if using. Cover with another slice of bread.
Cut your sandwich in half and serve immediately, or wrap it up for lunch on the go.