1. Whisk together first 3 ingredients in a large heavy saucepan. Gradually whisk in milk and whipping cream. Cook over medium heat, stirring constantly, 10 to 12 minutes or until mixture thickens slightly. Remove from heat.
2. Whisk egg yolk until slightly thickened. Gradually whisk about 1 cup hot cream mixture into yolk. Add yolk mixture to remaining cream mixture, whisking constantly. Whisk in vanilla bean paste. Cool 1 hour, stirring occasionally.
3. Meanwhile, cook peaches and corn syrup in a small saucepan over medium heat, stirring often, 4 to 5 minutes. Coarsely mash, and let cool 30 minutes. Stir peach mixture into cooled cream mixture.
4. Place plastic wrap directly on cream mixture, and chill 8 to 24 hours.
5. Meanwhile, melt butter in a small skillet over medium heat; add pecans, and cook, stirring constantly, 8 to 9 minutes or until toasted and fragrant. Remove from heat, and sprinkle with 1/4 tsp. kosher salt. Cool completely (about 30 minutes).
6. Pour chilled cream mixture into freezer container of a 1 1/2-qt. electric ice-cream maker, and freeze according to manufacturer's instructions. (Instructions and time may vary.) Before transferring ice cream to an airtight container for further freezing, stir in pecan mixture.
*Vanilla extract may be substituted.