Place the first 6 ingredients in a sided dish just large enough to hold the pork. Add the pork and turn to coat. Cover, refrigerate and marinate pork 4 hours, or overnight.
Preheat your grill to medium-high. Lightly oil the grill. Grill the pork 3 to 4 minutes per side, or until cooked through. Set pork on a cutting board and cool a few minutes.
While that occurs, spread buns with mayonnaise. Divide and set lettuce in each bun. Now thinly slice the pork and divide and mound in the buns. Top pork with carrot, cucumber, cilantro or mint, and hot sauce and serve.