Saute walnuts in small skillet over medium heat with the butter and sugar. Stir often, and watch carefully. Remove from heat as soon as the walnuts start to brown and caramelize.
Set walnuts on a piece of wax paper to cool.
Beat the cream cheese with the bleu cheese with a hand mixer until well blended.
Mound a teaspoon of cheese on each apricot half. Top with chopped walnuts, pressing into cheese. Refrigerate overnight. Serve at room temperature. Makes 32.