Prepare the Crust: Preheat oven to 325°F. Coat a 10-inch tart pan with a removable bottom with cooking spray. Stir together cracker crumbs, pecans, cacao nibs, brown sugar, and salt in a medium bowl. Stir in egg white and melted butter until combined. Spread mixture evenly in prepared tart pan, pushing into bottom and up sides of pan. Bake until set, about 15 minutes. Remove from oven; cool at least 15 minutes or up to 2 hours.

Meanwhile, prepare the Filling: Bring parsnips and milk to a boil in a medium saucepan over medium. Boil, stirring occasionally, until tender, 10 to 12 minutes. Pour mixture through a fine mesh strainer into a heatproof bowl; reserve strained milk. Place parsnips in a blender. Secure lid on blender, and remove center piece to allow steam to escape. Place a clean towel over opening. Process until smooth, about 1 minute, adding ½ cup to 1 cup strained milk until mixture is smooth. Measure parsnip puree to 1 cup. Discard remaining puree and strained milk, or reserve for another use. Whisk together parsnip puree, egg, buttermilk, brown sugar, salt, cinnamon, and nutmeg in a large bowl until smooth.

Pour Filling into cooled Crust. Place tart on a large rimmed baking sheet, and bake at 325°F until set, about 20 minutes. Transfer to a wire rack; let cool completely, about 1 hour. Remove tart from pan.

While the tart cools, prepare the Pan-Roasted Apples: Melt butter in a 10-inch cast-iron skillet over medium-high. Continue cooking, undisturbed, until light brown, about 2 minutes. Add apples, brown sugar, rosemary sprig, and lemon peel strip. Stir together, and spread mixture in an even layer. Transfer to oven, and bake at 325°F until tender, about 20 minutes. Remove and discard rosemary and lemon peel.

Dollop Spiced Apple Butter onto tart, and top with Pan-Roasted Apples.