In a medium bowl stir together flour, walnuts, Parmesan cheese, rosemary, baking powder, and salt. Using a pastry blender cut in shortening until flour mixture resembles fine crumbs. Make a well in center of flour mixture.
In a small bowl combine eggs and milk. Add to flour mixture all at once. Stir just until dough clings together.
On a lightly floured surface gently knead dough about 1 minute or until smooth. Divide dough in 24 portions; shape each portion in a ball. Cover dough; let rest for 20 minutes.
In a heavy 10-inch skillet pour cooking oil to a depth of 3/4 inch; heat to 375 degrees F. (Submerge end of thermometer in hot oil.) Meanwhile, on a lightly floured surface roll each ball in a 4-inch circle.
Fry dough circles, 2 or 3 at a time, in hot oil for 2 to 3 minutes or until golden, turning once. Drain on paper towels. (Keep warm on a baking sheet in a 300 degrees F oven while frying remaining fritters.) Serve with Garlic Mayonnaise. Makes 24 fritters.
In a small bowl stir together garlic, olive oil, and mayonnaise.