Combine the warm water, rice vinegar, sugar, and salt in a large airtight container. Whisk together until the sugar has dissolved. Add the fennel seeds and red onions. If the red onions are not covered, add additional rice vinegar.
Cover and place in the refrigerator for at least 30 minutes. The longer they are left to pickle, the more flavorful the red onion will become. Can be stored in the refrigerator for about 2 weeks.
Combine the dijon mustard and horseradish in a small bowl. Spread the mixture on a slice of white bread. Top that bread with salami and cheddar cheese. Top with a generous portion of pickled red onions. Place the three pieces of lettuce on top followed by the second piece of bread. Serve immediately.