In a small pot, heat the olive oil over medium low heat for about 30 seconds.
Add the minced garlic and stir quickly to let it brown just slightly, another minute more.
Add the flour and whisk together into a thick paste, allowing the raw flour to cook slightly.
Add mustard and whisk again—it will be very thick.
Whisking constantly, slowly pour the no beef stock into the pot, allowing it to combine with the roux (flour paste).
Place the sprig of fresh thyme into the gravy mix.
Bring to a simmer and then lower heat and allow to simmer until slightly thickened, about 5 more minutes.
Once it reaches your desired thickness remove from the heat and serve.