To make french toasts, chop parsley into small pieces.
In a medium bowl, whisk together eggs, heavy whipping cream, cheese, parsley, salt and pepper until well combined.
Heat ½ tablespoon of oil in a large skillet (I used 12-inch non-stick skillet) over medium high heat.
Dip bread slices in the egg mixture one at a time, piercing with a fork to thoroughly soak bread slices inside.
Reduce heat to medium.
Place 4-5 dipped bread slices in hot skillet and cook until golden brown, 3-4 minutes. Flip and cook the other side for another 2-3 minutes. Repeat with the remaining bread slices.
To make the topping, halve the cherry tomatoes and cut avocado into small pieces.
Combine tomatoes and avocado in a small bowl and drizzle with lime juice.
Serve french toasts warm topped with tomato avocado topping.