Whisk the sour cream, milk, and mustard in a small bowl and set aside.
In a small saucepan or deep skillet, heat enough water to cover eggs to a boil. Reduce the heat to a simmer. Crack the eggs, one at at time in a small bowl and drop each one into the pot carefully so to not splash. Cook for 3 to 5 minutes until the whites are set and the yolks are almost set. Remove the eggs gently with a slotted spoon.
Meanwhile, toast the muffin. Top with the ham and tomato slices and place in the toaster oven for another minute (or under the broiler).
Arrange the eggs over the sliced tomato and spoon a bit of the sour cream 'hollandaise' sauce over each.
Get fancy and win points for presentation by garnishing with chives and seasoning with salt and pepper.