Mix well using a whisk adding olive oil last and let stand at room temperature for 30 minutes. Re-season with salt if needed.
Sauté the shallots and celery in the olive oil until translucent.
Add garlic and saffron and sweat another minute until you can smell the garlic. Add the tomato paste and wine.
Simmer down until the mixture is reduced by half. Add mushrooms, season well and simmer for 20 minutes.
Cover and turn off heat.
Let cool to room temperature. Season with salt and pepper, add vinegar, fresh thyme and parsley.