Reduce the cider: In a small saucepan, simmer 3 cups apple cider until reduced to ⅓ cup. Cool completely.
Make the dough: In a large bowl, beat together the melted and cooled butter, granulated sugar, and brown sugar until smooth.
Add eggs, vanilla, and cooled cider reduction; beat until combined.
Add flour, cornstarch, salt, cream of tartar, baking soda, baking powder, cinnamon, and nutmeg. Mix until just combined -- be careful not to overmix.
Chill: Cover dough and refrigerate for 1 hour or up to overnight. The dough should be firm enough to scoop.
Prepare to bake: Preheat oven to 350°F. Line baking sheets with parchment paper. Mix rolling sugar and cinnamon in a small bowl.
Form cookies: Scoop 3 tablespoons dough per cookie, roll into balls, and coat in cinnamon-sugar mixture. Place 6–8 per tray with room to spread.
Bake: Bake 11–14 minutes, until edges are just set and centers look soft and underdone. Let cool fully on baking sheet before transferring.