Place cookies in a food processor; process until finely ground crumbs measure about 1 cup. Add oil; pulse to combine. Coat a 12-cup muffin tin well with cooking spray. Spoon about 1 packed tablespoon crumb mixture into each muffin cup; press crumbs firmly into bottom. Bake at 300° for 7 minutes or until lightly browned. Remove from oven; cool.
Wipe food processor clean. Place brown sugar, yogurt, and cream cheese in processor; process until smooth. Add vanilla, table salt, and eggs; process until smooth. Spoon about 3 tablespoons batter into each muffin cup. Bake at 300° 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.
Run a thin knife around outside edge of each cheesecake. Carefully remove cheesecakes from pan; place on a platter. Chill cheesecakes until ready to serve.
Combine granulated sugar and 2 tablespoons water in a medium, heavy saucepan over medium-high heat; cook until sugar 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 and 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. Spoon about 1 tablespoon caramel over each cheesecake. Sprinkle cheesecakes evenly with flake salt.