Rinse the salt-cured herring fillets under cold water to remove excess salt, then pat dry with a paper towel.
Slice the whole wheat rolls lengthwise and toast until lightly crisp and warmed through.
In a small bowl, mix the mayonnaise and Dijon mustard. Season with salt and black pepper.
Spread the mayonnaise–mustard mixture inside the toasted rolls.
Layer the minced onion, sliced pickles, chopped parsley, chopped chives, and herring fillets into the rolls to assemble the broodje haring.
Add the lemon slices to the sparkling water and gently stir. Add ice cubes.
Serve the broodje haring with potato chips, pickle spears, pear slices, and lemon sparkling.