Place the eggs in a saucepan of cold water over high heat. Bring to the boil, then reduce heat to low and simmer for 3 1/2 minutes. Remove the eggs and cool slightly. Peel carefully, then set aside.
Place the mayonnaise and Dijon mustard in a bowl, then add 1/3 cup (80ml) of boiling water. Whisk to make a loose dressing, adding a little more water, if needed.
Divide the cos lettuce between the 4 serving bowls and top with the cooked beetroot.
Carefully halve the soft-boiled eggs and sit them on top of the beetroot. Drizzle with the mustard dressing, season with some freshly ground black pepper and garnish with the chopped chives. Serve with some crusty bread.