Slice apricots in half.
Preheat grill to 350-400°. (Stove top method, grill apricots in a grill pan on the stovetop.)
Brush the inside of each half with olive oil.
Grill oiled-side down for 5-6 minutes.
Flip and grill the outside for three minutes.
Remove from grill, sprinkle with fresh thyme, and drizzle with olive oil.