Step 1: Boil water.
Step 2: Carefully take boiling water outside.
Step 3: Pour boiling water (well, very very hot water at this point) on the weeds, making sure to focus on the base/root of the plant.
Step 4: Wait a few days. The leaves eventually die back and the plant goes away. I'd show after pictures, but who wants to look at gravel?
You could be a bit more proactive than I was and cut back the plant first... but that would have required more effort. And I was genuinely curious how this would turn out on a large, stubborn weed.
|one of the large, stubborn weeds in question|