Prepare the tofu. Slice the tofu lengthwise into 4 slabs. Cover the tofu with a thin dish towel or several paper towels. Weight down the tofu with a heavy cookbook. Press for 20 minutes, changing the towels in between. Or use a tofu press. Now slice each of the 4 slabs lengthwise into about 8 slivers, so you have 32 slivers. Now cut each sliver into pea-sized cubs (very tiny cubes).
Make the dressing. In a large bowl, whisk together vegan mayo, relish, nutritional yeast, mustard, kala namak, turmeric, paprika, and black pepper to taste.
In a food processor, pulse together the capers, scallions, and dill until mixed up but still chunky. Or, use a knife to very finely chop the ingredients together.
Make the egg salad. Add the tofu cubes and the caper mixture to the mayo dressing. If using red onion, add it in as well. Stir gently to coat all the tofu pieces without crushing them. Taste for seasonings, adding a pinch of salt and black pepper as needed. Cover and refrigerate for 30 minutes (or more) before serving to allow the flavors to meld. If you're making egg salad sandwiches, make the avocado spread just before serving. Using a fork, mash the avocado in a bowl. Add salt and pepper to taste, a squeeze of lemon juice, and a touch of Dijon mustard. Taste, adding more lemon juice or mustard as desired. Lightly toast each slice of bread using a toaster, toaster oven, underneath your broiler, or in a frying pan with some oil or cooking spray.
Assemble the sandwiches. Spread some of the avocado spread on one slice of bread, then add your sandwich toppings of choice. Follow with a generous amount of the vegan egg salad. Top with the remaining slice of bread. Repeat with remaining bread. Serve with pickles on the side, if desired. If keeping leftovers, store the tofu salad separately (it will stay good in the fridge for 5 to 6 days).