Peel the carrots and cut into 5 mm thick slices. Peel the onions and cut into thin slices. Fry both in a pan in hot olive oil and cook covered for approx. 30 minutes over low heat. Add the garlic towards the end of the cooking time. Dust the flour and cook everything together for another 3 minutes while stirring. Remove from heat and stir in the boiling broth first, then the boiling milk. Season with the sugar, salt and pepper and nutmeg and cook for about 20 minutes without a lid (or until the liquid thickens). Whisk egg yolks with cream and stir in. Rock the pan back and forth over low heat until the egg yolk thickens. Add parsley before serving.
Tastes good with chops or roast chicken or as a vegetarian main course.