Heat a griddle, over a hot grill or burner, or pre-heat an indoor grill.
in a large bowl, combine arugula, half the pistachios, almonds and basil.
In a small bowl, whisk together vinegars, salt and pepper and 3 tablespoons of the olive oil.
Cut apricots in half and remove pits.
Brush cut side with remaining olive oil.
Grill for about 2 minutes on the cut side, until seared but intact.
Remove from the heat.
Toss together arugula mixture, dressing and half the apricots.
Arrange on a platter.
To serve, arrange the remaining apricots, cheese and remaining pistachios over the top.
