In a small bowl,combine sour cream,milk and mustard. Set aside. Lightly grease a medium skillet. Half-fill the skillet with water. Bring water to boiling. Reduce heat to simmering (bubbles should begin to break the surface of the water).
Break one of the eggs into a small dish. Carefully slide egg into simmering water, holding the lip of the dish as close to the water as possible. Repeat with the remaining egg,allowing each egg an equal amount of space.
Simmer uncovered for 3-5 minutes or until egg whites are completely set and yolks begin to thicken but are not hard. Meanwhile,place muffin halves (cut sides up) on a baking sheet. Broil 3-4 inches from the heat for 1-2 minutes or until toasted. Top muffin halves with ham and tomato slices.
Broil about 1 minute more or until toppings are heated through. To serve,use a slotted spoon to remove eggs from skillet. Place eggs on top of tomato slices. Spoon sauce over eggs.(if desired, sprinkle with chives)