For the ice cream: In a small, heavy-bottomed saucepot, bring the goat's milk and cream to a boil. Remove from the heat and whisk in the cheese, granulated sugar and salt. Blend the cheese mixture in a blender until smooth. Transfer to a bowl. Freeze the cheese mixture in an ice cream maker according to the manufacturer's instructions. Transfer to an airtight container and put in the freezer to harden, at least 2 hours. Let the ice cream soften 5 minutes before serving.
For the cherry vanilla sauce: Combine the cherries, orange juice, granulated sugar and cinnamon stick in a medium saucepan. Scrape in the seeds from the vanilla bean and add the bean. Bring to a boil over high heat, stirring until the sugar dissolves. Boil 1 minute. Strain into a bowl. Reserve the cherries. Return the juices from the bowl, cinnamon stick and vanilla bean to the same pan. Mix the cornstarch and 1 tablespoon water in a small bowl; stir into the juices in the pan. Stir over medium heat until the juices boil and thicken, about 1 minute. Mix in the reserved cherries. Chill the compote 2 hours.
For the walnuts: Preheat the oven to 250 degrees F. Lightly butter a large shallow pan.
Whisk together the egg white and 1 teaspoon water in a large bowl until frothy. Stir in the nuts. Stir together the brown sugar, cinnamon, nutmeg, allspice, pepper and cloves, and then stir into the nuts, coating well. Spread the nuts in the prepared pan and bake in the middle of the oven until dry, about 50 minutes. Cool and break into bite-size chunks.
For the whipped cream: Beat the cream, granulated sugar and vanilla in a medium bowl until peaks form. Stir in the thyme leaves.
To serve, scoop the ice cream into sundae bowls, top with cherry vanilla sauce, thyme whipped cream and chopped spiced walnuts.