Preheat outdoor or indoor grill or oven broiler.
Lightly coat the grill/broiler pan with olive oil. In a food processor or blender, combine first 10 ingredients (thyme through garlic); process until smooth.
Slice pork lengthwise, cutting almost (but not quite) through to the other side. Open the halves flat and rub with 3 tablespoons of dressing, reserving the remaining dressing.
Grill/broil pork for 10 minutes per side or until a meat thermometer registers 155 degrees when inserted in the thickest part.
Remove pork from grill and allow it to rest for about 5 minutes before cutting into 1/4-inch slices; coat with remaining dressing. Divide salad greens, pineapple, papaya (or mango) and pork among the dinner plates; serve.