Combine 1 c. sugar and ½ c. water in 1½-qt. heavy saucepan. Bring to a boil stirring constantly. If sugar crystals form on sides of pan, wipe them off. Add peanuts; cook and stir over low heat until syrup becomes grainy.
Remove from heat and pour into coarse sieve, reserving the loose sugar. Keep peanuts warm in oven that has been heated to 250° then turned off.
Place sugar removed in sieving with remaining ½ c. sugar and ½ c. water back into saucepan. Cook to the firm ball stage (245°).
Add peanuts to hot syrup and stir until syrup grains. Pour onto unbuttered baking sheet or marble slab and separate. When cool, store in covered container, in refrigerator or freezer.