Wash mushrooms, dry and slice. On a pan with a bottom diameter of about 24 cm, heat 1 tablespoon of butter, add diced onion and sauté until softened for about 3-4 minutes.
Increase heat, add mushrooms and stir occasionally, sauté for about 5 minutes until they release water.
Add diced pepper, season with salt and pepper and sauté for about 2-3 minutes.
Vigorously beat eggs with a fork with addition of milk, salt and pepper. Add sautéed ingredients from the pan and optionally diced ham and grated cheese. Mix with a spoon.
On the pan heat the second tablespoon of butter, spread it over the entire pan surface. Pour egg mixture with additions. Set low heat, cover the pan with a lid and heat until the mass sets for about 5 minutes. Alternatively - for an even better effect - after two minutes of sautéing (without a lid) you can also place the pan in an oven preheated to 180 degrees C.
Finally sprinkle with chopped chives. Omelette can be slid onto a plate and cut into portions.