Whisk egg and milk in a small bowl. Add the mixture to the pan and stir briefly to combine with the vegetables. Cook, tilting the pan and letting egg run under the edges, until the egg forms a thin, even layer. Continue to cook, reducing the heat if starting to brown, until just slightly wet, 1 to 2 minutes. Sprinkle with cheese and salt. Use a spatula to roll into an omelet. Serve topped with sour cream and chives.