Fill a large saucepan with 1” water and place a steamer basket inside. Bring water to a rolling boil, and use tongs to gently place eggs in steamer basket. Cover pan and steam eggs for 9 minutes.
While eggs steam, fill a medium bowl with ice water. When eggs are done, transfer immediately to ice water to cool completely.
Tap eggs all over on a countertop to crack shells, then peel and quarter lengthwise.
In a medium bowl whisk to combine sour cream, buttermilk, dill, chives, lemon juice, and salt.
On a serving platter, scatter romaine. Top with avocado, ham, tomatoes, cucumber, and eggs. Drizzle with dressing.