While the Healing Ring will give a little profit, it is not a good use of Nut Mixes which are quite rare.
Mystery Rings are a very good profit making item assuming you acquired the Broken Rings from drops rather than costly Rings. Requiring 12 ingredients is a considerable drawback however and in general Broken Rings are not worth bothering with until Endgame.
To farm the Broken Ring easily (but perhaps costly) bring as many Willpower Rings as you can into a low level dungeon, and then purposely get hit by the Orange Ropers, the ring will be used every time you get hit until it's broken, then replace it with another Willpower Ring and repeat.
It is worth noting that any ring with pluses prior to breaking and turning into a Broken Ring will not retain its plus value.