Place peaches in a large stockpot of boiling water; cook 1 minute. Drain and plunge peaches into ice water; drain. Peel peaches; coarsely chop.
Combine chopped peaches, sugar, and remaining ingredients in a large, heavy stockpot; bring to a boil, stirring occasionally. Reduce heat, and simmer until slightly thick and reduced to 6 cups (about 45 minutes), skimming the foam from surface of mixture occasionally. Cool; discard basil. Pour into an airtight container. (Mixture will thicken as it cools.) Cover and chill.
Note: Refrigerate jam in an airtight container for up to three weeks.