Clean the chanterelles. If you've never done it before, see the blog post for detailed instructions on that.
Chop the green onions into rings, grate the garlic cloves, remove the thyme and rosemary leaves from their stems and chop them finely.
Heat the oil in a non-stick pan. Add the mushrooms, green onions, garlic, and herbs to the pan and cook on high for a few minutes. Adjust the taste generously with salt and pepper. Remove from the pan and keep warm while you cook the eggs.
Wipe the pan clean with a paper towel. Melt the butter in the pan.
Whisk the eggs with the milk and some salt and pepper. Pour the egg mixture into the pan, turn the heat down to medium and cook the omelet until it's starting to get set. It depends on you how set you like it, it can still be a bit runny in the middle or it can be firmer if you prefer it that way.
When the omelet is almost set, add the chanterelle mixture on one half of the omelet. Using a wider spatula, fold the other half over the mushrooms. Turn the heat off and let the pan on the hob for another minute or two.
Cut in two pieces, sprinkle with parsley or chives and serve with bread and green salad.