I mean, it's not like you can run an experiment to determine if the dinosaurs were wiped out by an asteroid... I mean, what would that involve? Creating planets and populating them with dinosaurs, Jurassic-Park style, and then bombarding them with asteroids? Even if it were possible, it wouldn't really prove anything except whether the mechanism is feasible, it wouldn't determine whether that was actually what happened or not. So you can't really use an experiment.
What you CAN do is make predictions based on that hypothesis, and then make observations to see if the predictions are borne out. For one, you should see evidence of asteroid impact, things like iridium, shock-deformed quartz, microtektites, an impact crater, maybe even a tiny fragment of the asteroid itself... and in fact, after 30 years of looking, every single one of those things showed up, so we're pretty confident there was a giant asteroid impact. For another, you predict that the extinctions coincide with that impact if the impact caused them. And when you look at really abundant microfossils, stuff like fossil plankton and pollen, you can trace the Cretaceous stuff right up to the iridium layer that is the debris field, and then these species vanish forever. So the observations of geology, geochemistry, and paleontology are all consistent with predictions. The same process is used to test other hypotheses about historical processes, such as continental drift, or natural selection, or the formation of the solar system.
That's the *actual* scientific method. It's testing hypotheses against observation. Controlled experiment may or may not come into it at all.