To prepare dressing, combine all ingredients in a screw-top jar. Place lid on jar and shake well.
Slice apples into quarters, cut out core and stems, and then cut quarters into halves again. Toss with melted butter. Sprinkle lightly with salt, and toss.
Grill apples over a hot fire (direct heat), about 3 minutes per side, until they have golden grill marks. Don't let them blacken. Remove from grill and let cool. (Apples can remain at room temperature up to 1 hour.)
Place lettuce in a large bowl. Top with nuts and cheese. Shake dressing well, and drizzle over salad. Top with warm apples and garnish with grapes or clementines, if using.