Heat 1 tsp / 5 ml of olive oil in a heavy-bottomed pan over medium heat.
Add the onion, carrot, celery, thyme, and sage.
Sauté, stirring occasionally, until the vegetables are soft and beginning to turn golden, about 3 to 5 minutes.
Push the vegetables to one side of the pan.
Add the remaining 1 tsp / 5 ml of olive oil to the empty side, then add the sliced mushrooms.
Cook the mushrooms, stirring only occasionally, until they are lightly browned and have released their moisture, about 3 to 5 minutes.
Pour in the wine to deglaze the pan, stirring and scraping up any flavorful browned bits from the bottom.
Stir in 3 cups / 710 ml of the broth, the Braggs Liquid Aminos, and the Worcestershire sauce.
Bring the mixture to a simmer, then cover and cook for 3 minutes.
In a small bowl, whisk together the remaining 3 Tbsp / 45 ml of broth with the arrowroot powder to create a slurry.
While continuously whisking the gravy in the pan, slowly pour in the arrowroot slurry.
Continue to cook and whisk until the gravy thickens, which will happen very quickly.
Remove from the heat.
Taste and season with salt and pepper as needed before serving.
When adding the wine, be sure to scrape the bottom of the pan to lift all the flavorful caramelized bits (the fond) into the gravy.
