Gather all the ingredients. Adjust an oven rack to the middle position and preheat the oven to 425ºF (220ºC). For a convection oven, reduce cooking temperature by 25ºF (15ºC).
To Make Shortcut Espagnole Sauce
Cut the onion, celery, and carrot into small chunks.
In the Dutch oven (or oven-safe heavy bottom pot), add 1 Tbsp olive oil. When the pot is hot, add chopped onion, celery, and carrot.
Season with ½ tsp kosher salt and freshly ground black pepper. Sauté for 3 minutes.
Pop in the oven and roast at 425ºF (220ºC) for 20 minutes.
Meanwhile, prepare bouquet garni. You can use a disposable mesh tea bag (left) or a cheese cloth (right).
Here I encase 1 bay leaf, 1 tsp dried thyme, 3 sprigs parsley, and 8 peppercorns in the cheesecloth.
Tie the corners tightly.
Transfer the pot from the oven to the stove. Add 1 Tbsp tomato paste and mix well.
Add 4 Tbsp red wine and 8 cups beef stock and mix to combine.
Add bouquet garni and bring it to boil.
Once boiling, lower the heat and simmer for 1.5 hours, until roughly 3 cups of broth remained in the pot. You can skim the foam and scum during reducing. I fill water in a measuring cup with a pout to clean the fine mesh skimmer.
If you are using this Demi-Glace for Hayashi Rice, you can start cooking rice and marinating beef. About 30 minutes before finishing the reduction process, start making Brown Roux.
To Make Brown Roux
In a small saucepan, melt 2 Tbsp butter over medium heat. Add 4 Tbsp flour.
With the silicone spatula, combine well. At first, it will turn into a crumble-like texture.
Then it will turn into foam and liquid. Continue to cook for 12-15 minutes, or until the color turns brown, like chocolate.
Set aside and wait until the Espagnole sauce is finished.
To Combine Espagnole Sauce and Brown Roux
After cooking for 1.5 hours, the Espagnole sauce has been reduced. You will need 3 cups of the sauce by straining the vegetables.
Set the 3 cups aside. You can freeze the rest of the Espagnole sauce for future use.
When you have the brown roux ready, put the pot back on the stove on low heat. Gradually add the Espagnole sauce to the brown roux and combine well before you add more sauce.
Once you add all 3 cups, and mix well together, the Demi-Glace is ready to use! Set aside for your recipe.