First, the bad news: What you've been calling a shawarma probably isn't. VivreManger knows from shawarmas, and the thing you get with meat sliced off a big, rotating cone of "mystery meat" (usually produced, nationwide, by Chicago's Kronos Foods), that ain't it.
VivreManger explains: "In my experience the original shawarma (Arabic) / doner kebab (Turkish) / gyro (Greek) should be made of marinated and spiced slices of lamb, heavily interleaved with a healthy quantity of lamb fat. The result is pressed, placed on a heavy strong skewer and slowly rotated to yield a result that is simultaneously gently cooked at the core and singed to yield an intensely browned flavorful taste at the fat-laden periphery, the Maillard reaction. To achieve that last effect, the external heat source must produce a temperature of at least 300 and preferably 500 degrees Fahrenheit."
However, you almost never get that in the States. "Unfortunately the Greek version, most commonly available in the U.S., the Kronos gyro, has completely ruined the market for this product by adulterating its taste," complains Vivre. "The Kronos gyro is prepared either as Spam on a stick or Spam on a grill. Instead of slicing meat and fat and threading it together through the spit, Kronos grinds it into a spiced mess, a Spam-like mold, that can be cooked in a variety of ways, whose result is remote from the original." So you get a bland-wich, distinguished by spicy condiments that cover up the taste.
Where can you get the real thing in Boston? VivreManger cautiously recommends Brookline Family Restaurant: "not bad, but not great either." Other hounds seem to like it just fine, no complaints. Sofra also has a great lamb shawarma, says newhound, "but it's totally unlike what you are considering authentic. Theirs is made with meltingly tender braised lamb."
Brookline Family Restaurant [South Shore]
305 Washington Street, Brookline
1 Belmont Street, Cambridge