Prep the avocado base: Scoop the avocado into a bowl. Mash until mostly smooth with a few small chunks for texture.
Mix the tuna salad: Add the drained tuna, mayonnaise (if using), mustard, lemon juice, celery, red onion, and garlic.
Season with salt, pepper, and red pepper flakes. Stir until well combined. Taste and adjust with more lemon, salt, or pepper.
Assemble the sandwiches: Lay out the bread slices.
Spread a thin layer of butter on the outside of each slice for crisp browning. On the inside, pile the tuna mixture evenly over two slices. Top with herbs (if using) and lay cheese slices over the tuna.
Close with the remaining bread, buttered side out.
Stovetop method: Heat a skillet over medium heat. Add a little butter or oil. Place the sandwiches in the pan and cook 3–4 minutes per side, pressing gently with a spatula, until the bread is golden and the cheese is melted.
Lower the heat if the bread browns too quickly.
Oven or broiler method: Preheat the oven to 400°F (200°C) or set the broiler to high. Place open-faced sandwiches on a baking sheet (tuna and cheese on top, no top slice). Bake 6–8 minutes or broil 2–4 minutes until the cheese is bubbly and the edges are crisp.
Add the top slice if you like and toast briefly.
Air fryer method: Air fry at 375°F (190°C) for 5–7 minutes, flipping halfway, until the cheese melts and the bread is golden.
Serve: Let the sandwiches rest 1–2 minutes so the filling sets. Slice in half. Add tomato slices or pickles on the side if you like.