Whisk eggs and milk together in a medium size bowl, season with sea salt and freshly ground black pepper.
Slice avocado into thin wedges, place avocado, parmesan and parsley in a small bowl. Set aside.
Heat a large non-stick frying pan over a medium heat, brush with a little melted butter. Cooking two at a time, dip slices of bread into the egg mixture for 10 seconds each side. Cook for 2 minutes each side or until golden. Transfer to a plate and keep warm. Repeat with remaining bread, brushing pan with a little more butter as needed.
To serve, place 2 slices of french toast on each plate. Top with some of the avocado salad. Serve immediately.