Heat olive oil over medium heat in a medium saucepan. Sprinkle flour over oil, and cook, whisking to combine, until the mixture smells nutty and toasted, 2 to 3 minutes. Add soy sauce and nutritional yeast, whisking to combine. The mixture will seize up and get chunky.
Slowly add vegetable stock to the pan, whisking constantly, until the stock is fully incorporated into the flour mixture and is very smooth. Increase the heat to medium-high and cook, whisking often, until the mixture thickens and can coat the back of a spoon (add more stock if the gravy gets too thick), 8 to 10 minutes. Whisk in poultry seasoning and mustard. Serve warm.