Combine 1-1/2 cups flour, sugar, undissolved yeast and salt in a large mixer bowl. Heat water, sour cream, and butter until very warm (120° to 130°F). Gradually add to flour mixture. Beat 2 minutes at medium speed of electric mixer, scraping bowl occasionally. Add eggs and 1 cup flour; beat 2 minutes at high speed. Stir in remaining flour to make a stiff batter. Cover tightly with plastic wrap; refrigerate 2 to 24 hours.
Remove dough from refrigerator. Divide into 24 equal pieces; shape each into a ball. Cover; let rest 15 minutes. Place balls on greased baking sheets 2 inches apart. Make a deep and wide indentation on each ball by pushing outward toward edge, leaving 1/2-inch ridge around outside. Fill with 1-1/2 tablespoons Apricot Filling. Cover; let rise in warm, draft-free place until doubled in size, about 1 hour.
Bake at 350°F for 17 to 22 minutes or until done, rotating pans halfway through baking. Remove from baking sheets; cool on wire racks.
Apricot Filling: Combine 1-1/2 cups apricot preserves, 1-1/2 cups flaked, sweetened coconut and 1-1/2 cups chopped walnuts in a small bowl. Stir to blend.