In a small saucepan, bring 1 cup water to a boil. Add saffron and boil 2 minutes. Let cool to room temperature. Use a sharp knife to cut Parmigiano-Reggiano into thin slices. Cheese will not cut evenly, but any shape 2 to 3 inches long and no more than 1/4 inch thick will work well. In a small bowl combine cheese with saffron liquid and marinate 6 hours.
In a deep-fryer heat oil to 365 degrees. In a bowl beat egg yolk; add water, stirring lightly to blend. Add 1 1/2 cups flour all at once and stir gently with a fork or chopstick until just blended. Do not overblend; batter will be lumpy. Piece by piece, coat cheese pieces with extra flour; dip pieces thoroughly in batter, then quickly toss in hot oil (don't wait for extra batter to drip off). Cook 2 to 3 minutes, turning occasionally, until golden and crisp. Using a slotted spoon, scoop up cheese and drain on paper towels. Keep warm while you fry remainder. Sprinkle with salt and serve immediately.