Transfer the eggs to a bowl and add chopped onion, mayonnaise, mustard, chives, dill, nutritional yeast, salt, and pepper

Gently fold everything together until the mixture looks smooth, creamy, and evenly combined

Spoon the egg salad generously onto two slices of bread, spreading it evenly to the edges

Sprinkle grated Parmesan cheese over the egg mixture for a savory layer

Place the remaining bread slices on top and press lightly to hold everything together

Heat butter in a pan over medium heat until melted and slightly bubbling

Place the sandwiches in the pan and cook until the bread turns golden brown and crisp

Flip carefully and cook the other side until both sides are toasted and fragrant

Remove from the pan, let cool slightly, then slice and serve warm