Cook onion and garlic in oil in a 3 to 4-quart heavy pot over moderate heat, stirring, until golden, about 8 minutes. Stir in remaining ingredients except pork, lavash, and coleslaw and simmer, covered, 10 minutes. Add pork and simmer, covered, turning occasionally, until tender, about 45 minutes.
Transfer pork with tongs to a cutting board. Puree cooking liquid in a blender until smooth (use caution when blending hot liquids) and return to pot. When pork is cool enough to handle, shred lengthwise with your fingers or 2 forks and add to sauce. Simmer, stirring, just until pork is heated through.
Divide shredded pork among pieces of lavash and top with some coleslaw, then wrap lavash around to form a cone.
Shredded pork in sauce can be made 1 day ahead and chilled, covered. Reheat before using.