Toast the bread. Set on individual plates. Half the avocado, remove the pit and peel, and cut each half into thin slices. Lay on the toast, and mash with a fork.
Top with tomato slices. Sprinkle with a little pinch of salt and pepper.
Poach the egg. By now, your water should be boiling. Reduce the heat to low, until your water is barely moving, with only a few small bubbles rising to the surface. Crack eggs into the water, hovering right over the surface so that the eggs don’t have very far to drop. Cook for 3 minutes for a very runny yolk or 3 1/2 minutes for thicker (yet still runny) yolk.
Remove eggs from water with a slotted spoon and place atop tomato.
Spoon avocado hollandaise over the top. Sprinkle with parsley and/or chives if using along with a pinch of salt, and a generous pinch of pepper.