Drizzle the nectarine halves with a little olive oil. Grill cut-side down for 2 to 3 minutes, turning midway to achieve lovely grill marks. Set aside.
In a bowl, whisk together the honey, Dijon and vinegar. Whisk in the olive oil to emulsify. Add some salt and pepper and mix.
Toast the slivered almonds in a small skillet over medium-low heat until just turning golden brown.
In a large bowl, toss the salad greens with enough of the dressing to lightly coat. (You won't use all of the dressing; save to have on another salad tomorrow!) Toss in the warm toasted almonds.
Divide the salad among 4 plates. Place a nectarine half on each serving. Drizzle the nectarines with a little more dressing. With a fork, cut the blue cheese into chunks and distribute among the plates.
Grill more fruit if you'd like each plate to have two halves instead.