Roughly chop the onion, garlic, carrot, and mushrooms.

Heat the cooking oil in a pot over medium heat.

Fry the chopped vegetables for 5 to 8 minutes, stirring occasionally.

Add the 2 tablespoons tomato paste and 2 tablespoons all-purpose flour.

Stir the tomato paste and flour into the vegetables until evenly coated.

Pour in the 1/4 cup red wine to deglaze the pot.

Scrape the browned bits from the bottom of the pot as the wine reduces briefly.

Add the 2 cups water, 1 tablespoon soy sauce, and 1 tablespoon mustard.

Add the bay leaves, dried thyme, salt, black pepper, and a pinch of sugar.

Bring the mixture to a gentle simmer.

Simmer the gravy for 10 to 15 minutes until the vegetables are very soft and the flavors develop.

Place the fine-mesh sieve over a heatproof bowl.

Strain the gravy through the sieve, pressing the cooked vegetables to extract the liquid.

Return the strained gravy to the pot and heat it gently.

Simmer briefly until the gravy thickens to the desired consistency, then serve warm.