Line a 10‑inch (25 cm) baking dish with parchment paper.
Mash the avocado in a mixing bowl until smooth.
Add the eggs and cream cheese and mix until creamy.
Stir in the oats and shredded hard cheese.
Add the baking soda, baking powder, salt, black pepper and chopped parsley, then mix until everything is fully combined.
Transfer the mixture to the lined baking dish and spread it evenly.
Bake at 350°F (180°C) for about 25 minutes, until set and golden on top.
Let the bread cool slightly, then lift it out, slice and serve warm or at room temperature.