To make dressing – place mustard, honey and vinegar in a mini-food processor or blender and process until combined. With the motor running, pour oil in a steady stream until emulsified. Add salt and pepper to taste. (You can also do this in a bowl with a whisk, just take care to fully incorporate the honey.)
Preheat a grill to medium. Cut peaches in half and remove pit. Cut into quarters if they're large. Brush with oil and grill until just charred, about 3-5 minutes. You can grill the other side if you like. I like to grill apricot halves and cut in half again after they're off the grill.
Place spinach in a serving bowl or platter and toss with just enough dressing to coat lightly. Top with grilled fruit and nuts. Drizzle with any remaining dressing, if desired.