Activate Mirror Image using Civilized Scholar's ability by tapping it.
Resolve that ability and choose to modify it with dredge, causing you to mill at least one card, return the creature card with dredge from your graveyard to your hand, then discard that same card, untap Mirror Image and fail to transform it.
Repeat.
This quirky loop hinges on Mirror Image copying Civilized Scholar, allowing the clone to inherit the original's tap ability while retaining its own identity as a separate permanent that cannot transform. By utilizing dredge on the discard phase of Civilized Scholar's ability, you feed your graveyard while repeatedly discarding the dredged card to instantly untap Mirror Image without advancing the turn. This creates an endless cycle of self-mill and discard triggers right from beneath your opponents' noses.