Finely chop the onion. Heat the oil in the pan and gently sauté the onion until soft. Add the hearts and the garlic, then stir for a couple of minutes. When the hearts change colour, add the wine, then turn up the heat and reduce it by half.
Cut the mushroom in half and add to the hearts. Stir through then add the stock, thyme, tomato, bay leaf and carrot (whole). Bring to the boil, then turn down the heat and simmer for about half an hour.
Remove the lid and cook until the sauce has thickened (for about 15 minutes).
Slice the carrot, season with salt and pepper to your liking, then scatter some fresh parsley over it.
Serve warm.