Heat oil in a wide saucepan and sauté the onion on medium heat until it is transparent.
Add the garlic and cook another minute while stirring.
Add the beef and break up, stirring continuously until it is browned all over.
Add the carrots, celery and mushrooms and cook, stirring occasionally, for 5 minutes.
Add remaining ingredients except parsley and cook, covered, for 20 minutes.
Taste and adjust seasoning if necessary.
The savoury mince is now ready to serve with the parsley sprinkled on top.
If preferred, it can be thickened with a little flour or just remove the lid from the saucepan and continue cooking slowly until the excess liquid has evaporated.
