Heat a grill pan over medium-high heat. Using your hands, rub the apricots all over with the oil. Grill, cut side down, for about a minute, until golden brown grill marks are visible when apricots are lifted with a spatula. Turn and grill the other side for about 25 seconds, or until brown grill marks are visible when lifted. Transfer to a platter, cut side up.
Divide the crumbled goat cheese evenly on top of each apricot half. Scatter the blueberries on and around the apricots. Drizzle with the honey. Garnish with mint leaves if desired. Serve immediately or within a couple of hours.