Hi June,
I make an appetizer similar to what you requested, during the Holiday Season:

APRICOT-GORGONZOLA BITES,

Soften dried apricot halves in some orange juice and then pat dry.

Top each apricot half with Gorgonzola cheese thinned with half & half or some softened cream cheese.

Then top each one with a pistachio.

I don't see why you couldn't do the same thing with a fresh apricot. I'll bet it would taste even better! Let us know.