Preheat oven to 400 degrees. Add diced apple, bourbon, brown sugar, cinnamon, nutmeg and allspice in a medium sized bowl and mix to combine. Transfer to a small baking dish and roast for about 45 minutes or until apples are tender, stirring mixture once or twice throughout cooking process. Remove from oven and allow to cool slightly, then transfer to a small food processor and puree until smooth but slightly chunky in texture. Set aside.

Bring half and half, vanilla extract, cinnamon stick and salt to a simmer in a heavy bottomed saucepan over medium heat, stirring occasionally. Remove from heat, cover and allow to steep for 20 minutes.

Whisk egg yolks and sugar in a medium sized bowl until pale and fluffy. Gradually whisk warm cream mixture into yolk mixture, then transfer mixture back into saucepan. Heat over medium low heat, stirring often, until custard thickens and temperature reaches about 170 degrees. Remove from heat, discard cinnamon stick and stir in heavy cream and bourbon. Transfer into a bowl set over an ice bath or place in the refrigerator for a few hours to chill.

Freeze in an ice ream maker according to manufacturer's instructions. After about 10 minutes or when ice cream has partially frozen, gradually add roasted apple mixture and candied pecans, little by little, for a swirl effect. Transfer to a container and freeze until solid.