Coarsely mash nectarines with 1/3 cup sugar in a medium saucepan, using a potato masher. Let stand until very juicy, at least 15 minutes.
Meanwhile, whisk together remaining 1/3 cup sugar and the cornstarch in another medium saucepan. Add whole milk, buttermilk, cream, salt, and honey; whisk until blended. Bring to a boil over medium heat, stirring often, then reduce heat and simmer 2 minutes, continuing to stir. Set pan in a bowl of ice water and stir often until cool. Chill until needed.
Bring nectarines to simmering over medium heat, stirring often, and cook until fruit is almost jammy in consistency, 10 to 15 minutes. Remove from heat and stir in rose water. Set pan in a bowl of ice water and stir often until cold.
Stir cream mixture into fruit mixture. Freeze in an ice cream maker according to manufacturer's instructions. Transfer to an airtight container and freeze until firm enough to scoop, at least 2 1/2 hours.
*Find with cocktail or baking supplies.
Make ahead: The milk base (step 2), up to 2 days, chilled.