Watching my husband play through (we're taking turns.) I had played both quests, but he played them back-to-back, which made the correspondences very obvious.
First: there's an abandoned house in Markarth, in which, it turns out, is a shrine to Molag Bal. This shrine has been desecrated by a priest of Boethiah. The player is tasked by Molag Bal to go fetch the priest, then beat him until he submits to Molag Bal, then beat him to death with Molag Bal's mace while he crouches in submission.
Second: the final battle of the Civil War, Stormcloaks side. The player beats General Tullius into submission. Ulfric then asks the player to kill the crouching Tullius with his own sword "to make a cool story."
If you're unclear about what mantling is and how it operates, that's what it looks like. Oh, Ulfric is leaving out a few ingredients - he needs a source of power, for one thing. But he's got a very good start here to channeling the power of Molag Bal as the Tribunal once channeled the power of the Anticipations. All you really need to do is to do something vile and disgusting - just like Molag Bal would do it!