Salted Potato-Caramel Cheesecake Gratins

Serves 10
1 medium baking potato, peeled and cut into ¼-inch-thick slices (about 1½ cups)
1 medium sweet potato, peeled and cut into ¼-inch-thick slices (about 2 cups)
1 quart no-salt-added chicken stock (such as Swanson)
15 vanilla wafers
2 tablespoons canola oil
1½ tablespoons all-purpose flour
2 garlic cloves, crushed
¾ cup 2% reduced-fat milk
1 thyme sprig
³⁄₈ teaspoon kosher salt, divided
¹⁄₈ teaspoon freshly ground black pepper
1½ ounces aged Gruyère cheese, shredded (about 6 tablespoons)
Cooking spray
⅓ cup packed light brown sugar
⅓ cup plain fat-free Greek yogurt
6 ounces ⅓-less-fat cream cheese, softened
¾ teaspoon vanilla extract
¹⁄₈ teaspoon table salt
1 large egg
1 tablespoon chopped fresh chives, divided
¾ teaspoon chopped fresh thyme
¼ cup granulated sugar
1 tablespoon water
½ tablespoon butter
¼ cup evaporated milk
½ ounce fresh Parmiggiano-Reggiano cheese, grated (about ¼ cup)
¼ teaspoon flake salt

1. Preheat oven to 325˚.
2. Place potatoes in a large stockpot; cover with stock.  Bring mixture to a boil; cook 4 minutes.  Remove from heat.  Carefully remove potatoes from pot using a slotted spoon, reserving cooking liquid.  Arrange potato slices in a single layer on a jelly-roll pan; set aside.  Strain cooking liquid through a fine-mesh sieve over a bowl; reserve ½ cup cooking liquid.  Discard solids and remaining cooking liquid.
3. Place cookies in a food processor; process until finely ground crumbs measure about ½ cup.  Heat a medium saucepan over medium heat.  Add oil to pan.  Sprinkle over oil; cook 1 minute, stirring constantly with a whisk.  Add garlic; cook 2 minutes, stirring frequently.  Combine milk and reserved cooking liquid.  Gradually pour milk mixture into flour mixture in pan, stirring constantly with a whisk.  Add thyme sprig to pan.  Bring mixture to a boil; cook 4 minutes or until slightly thick, stirring frequently.  Remove from heat.  Strain mixture through a fine-mesh sieve over a bowl, reserving liquid; discard solids.  Stir ¼ teaspoon kosher salt, pepper, cookie crumbs, and Gruyère cheese into milk mixture.
4. Coat a 10-cup muffin tin well with cooking spray.  Evenly divide ½ cup crumb mixture among muffin cups, reserving the rest; press crumb mixture firmly into bottom.  Bake at 325˚ for 7 minutes or until lightly browned.  Remove from oven; cool.
5. Wipe food processor clean.  Place brown sugar, yogurt, and cream cheese in processor; process until smooth.  Add vanilla, potatoes, table salt, and egg; process until smooth.  Spoon batter evenly between muffin cups.  Sprinkle evenly with remaining kosher salt, ½ tablespoon chives, and chopped thyme.  Bake at 325˚ for 18 minutes or until centers of cheesecakes barely move when pan is touched.  Remove pan from oven; cool on a wire rack to room temperature.  Cover pan; refrigerate cheesecakes 3 hours or until well chilled.
6. Combine granulated sugar and water in a medium, heavy saucepan over medium-high heat; cook until suhgar dissolves, stirring gently as needed to dissolve sugar evenly (about 3 minutes).  Continue cooking 12 minutes or until the color of light brown sugar (do not stir).  Remove from heat; carefully stir in butter, remaining crumb mixture, and evaporated milk (caramelized sugar will harden and stick to spoon).  Place pan over medium-high heat until caramelized sugar melts. Bring to a boil; cook 1 minute.  Remove pan from heat; cool caramel to room temperature.  Cover and chill 1 hour or until slightly thickened.
7. Spoon sauce mixture evenly over cheesecakes. Sprinkle with Parmiggiano-Reggiano cheese.  Bake at 325˚ for 1 hour or until cheesecakes are tender when pierced with a knife.
8. Remove cheesecakes from oven.  Preheat broiler to high.
9. Place cheesecakes in oven.  Broil cheesecakes 3 minutes or until browned.  Run a thin knife around outside edge of each cheesecake.  Carefully remove cheesecakes from pan; place on a platter.  Sprinkle with flake salt and remaining chives.  Chill cheesecakes until ready to serve.