Cut off stems of artichokes flush with bottoms; discard. Using kitchen scissors, trim outer 3 layers of leaves to 2 inches.
Fill a large stockpot with 2 inches of water. Set a steamer basket over water. Stand artichokes upright in basket; cover pot. Bring to a boil. Steam until bottoms of artichokes are tender when pierced with the tip of a knife, 30 to 40 minutes.
Remove artichokes from pot; let stand until cool enough to handle. Remove and discard inner leaves, leaving trimmed outer leaves to create a flowerlike shape. Using a teaspoon, remove fuzzy choke and any purple leaves; discard. Gently spread apart artichoke leaves to create desired appearance. Season with salt and pepper. Cover to keep warm.
Fill a large saucepan with 4 inches of water; bring to a boil. Reduce heat to medium. When water is barely simmering, break 1 egg into a small heatproof bowl. Gently tip bowl to slide egg carefully into water in pan. Repeat with remaining eggs. Cook until whites are set but yolks are still soft, 2 to 3 minutes. Lift out eggs with a slotted spoon; briefly rest spoon on paper towels to drain eggs.
Immediately spoon 1 egg inside each artichoke (be careful not to pierce yolk). Spoon about 1 tablespoon hollandaise sauce over top of each egg. Drape 1 slice salmon on top. Serve with hollandaise.