Add the artichokes, avocado, lime juice, salt and pepper to a food processor.
Blend until smooth, set aside.
Toast the olive bread slices.
Spread an even layer of the artichoke, avocado purée onto each slice.
Bring a pan ⅓ full of water to a simmer, add a dash of white vinegar.
Add each egg to small bowls.
Swirl the water and pour in 1 egg to the center.
Do not let the water boil, poach for 4 minutes.
Drain the egg using a slotted spoon onto a paper towel.
Top each of the toast slices with an egg and garnish with arugula, serve immediately.