Combine 2 cups all-purpose flour, undissolved yeast, and salt in a large mixing bowl. Heat water, honey and oil until very warm (120° to 130°F). Add to flour mixture. Beat 2 minutes at medium speed of an electric mixer.
Reduce speed to low; beat in mayonnaise, 2 eggs and whole wheat flour. Beat at medium speed 2 minutes. Stir in 3 to 3-1/2 cups flour until dough is easy to handle.
Knead on lightly floured surface until smooth and elastic, about 10 minutes, adding remaining flour if necessary. Cover; let rest 10 minutes.
Punch dough down; divide into thirds. Working with one third at a time, divide each third into 36 pieces. Shape each piece into a 1-inch ball. Place 3 balls in each of 36 greased (2-1/2-inch) muffin pan cups. Cover; let rise in warm draft-free place until doubled in size, about 35 minutes.
Beat remaining egg slightly; brush on rolls. Sprinkle with poppy seeds. Bake at 375°F for 12 to 17 minutes or until golden brown. Remove from pans. Serve warm. Or allow rolls to cool completely, store in tightly closed container and freeze for up to 1 month.
TIP: If using dark nonstick muffin pans, rolls will brown quickly. Check for doneness at minimum bake time.