"rofl-stomping" doesn't fit in the usual list of goals in conflict. Iran's likely goal is to be the biggest pain in the arse possible, and they have the deck stacked in their favour:
21% of the worlds oil flows through that strait, and it'll take anywhere from a week to a month to clear the mines (a week for a narrow, sort-of-safe channel, but what insurer would accept a 10% chance they lose the ship?). That's without iranian forces interrupting the MCM, or targeting tankers in other regions near the iranian coast (ASM launchers won't last longer than their first salvo, but that's a lot of missiles in the air. You can't reliably get them before they fire either, as iraqi scuds proved - and scuds are larger than ASMs). For reference the 1979 oil crisis only involved a 4% drop in oil production, and lead to a doubling of the price of oil.
The US options to respond are pretty short of a rofl-stomp - they can muster a small air & naval campaign at best with the forces available. The first gulf war involved thousands of aircraft (compare to the few squadrons moved to the region recently), and even with a ground campaign saddam wasn't replaced. They could sink most of the iranian naval assets, probably enforce air superiority over the important bits, pop most of the ASM launchers, and might as well strike the nuclear facilities, but what's the end-state? How do they get the iranians to stop fighting, short of a total occupation (something that would be several times larger than gulf war 2)? ASMs have shown up in the hands of non-state actors, so a bloodied state actor like iran could dangle the credible threat of ASM strikes on nearby shipping for the foreseeable future even with a constant US fast jet presence.
Autonomous mine countermeasures has the potential to greatly improve MCM speed, but it's not ready today in the numbers needed and doesn't solve the ASM issue.