Perhaps the consistency aspect comes down to technique, but a technique that includes more than just "right" notes and perfect fingerwork. Technique encompasses musicianship, as well: a well thought out phrase, audible dynamic shaping, an unfaltering, but ebbing and flowing, sense for rhythm. Great technique, because it is the most efficient way of realizing the musical score, lends a certain effortlessness to one's performance. So too, with cooking: the precise dice of onions, a natural understanding for a pinch of salt here or there, an awareness for the big picture (that all day project of playing nurse to a perfect stock), these things ensure quality regardless of the menu itself.
On a superficial level, variety, in music, comes with repertoire selection. On a deeper level, variety reveals itself in technique: articulation and pedaling transcend a purely technical function when heard in the context of, say, several Chopin preludes. A variety--the breadth of a performer's creative imaginings--begins here, with technique. In performance, a Chopin "specialist" must engage an audience by offering a multiplicity of flavors and tastes. I can hear the high praise: "she played a whole program of Chopin, beautifully, perfectly, but more than that, her playing never sounded the same from piece to piece."
Any artist capable of revealing a varied palette within a very focused repertoire should have no difficulties crossing over to other "cuisines." Don't be fooled by the menu; study the skill on the plate, if you can.