In a soup pot heat oil and butter.
Saute garlic, onions and dried thyme for 2 minutes.
Add flour and stir constantly for a minute on medium-low making sure not to brown the rue. If necessary add a few tablespoons of water.
Next, add in a cup of the stock - continue to stir until the flour is absorbed and the sauce thickens.
Add in the vegetables, chicken, and stock.
Season with salt and pepper.
Continue to cook on medium for about 10 minutes until the chicken is cooked.
Add in the parsley.
Lastly, add the cream.
Check seasoning and consistency. Add more salt and pepper or water if needed.
Switch the heat off and keep warm.