Put basil leaves, sugar, and lemon juice into a small saucepan and bruise leaves by mashing with a wooden spoon. Add 12 oz (1-1/2 cups) nectar and bring just to a simmer, stirring until sugar is dissolved. Remove from heat and let stand 5 minutes, then pour through a medium mesh sieve into a heatproof pitcher, discarding basil leaves. Stir in wine, peach, another 1-1/2 cups nectar, and basil sprigs. Chill, covered, at least 1 hour and up to 24. Serve over ice.
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