Preheat oven to 400°F (200°C).
Cut the avocado in half and remove the pit.
Use a spoon to slightly enlarge the cavity if needed.
Brush avocado halves with lemon juice.
Carefully crack one egg into each avocado half.
Season with salt and black pepper.
Remove any excess egg white if necessary so the egg fits neatly.
Place avocado halves in a small baking dish to keep them stable.
Bake for:
25–30 minutes for runny yolks
30–40 minutes for soft yolks
40–45 minutes for firm yolks
While the avocado bakes, melt 1 tablespoon butter in a skillet over medium heat.
Add diced tomato and shallots.
Cook until most of the tomato moisture evaporates.
Add vegetable broth and white vinegar.
Simmer until reduced by about half.
Remove from heat.
Gradually whisk in remaining cold butter, one tablespoon at a time.
Add egg yolks and whisk continuously until smooth and creamy.
Stir in lemon juice, tarragon, parsley, and red pepper flakes if using.
Remove the Baked Avocado Eggs from the oven.
Spoon tomato herb hollandaise over the top.
Garnish with extra tomato, shallots, and parsley before serving.