Heat oil in a saucepan over medium heat. Place apple pieces in saucepan; cook and stir until they are slightly caramelized, about 2 minutes.
Stir brown sugar into apples; cook, stirring constantly, until the mixture starts to bubble, about 2 minutes.
Pour apple cider vinegar into saucepan. Reduce heat to low and cover. Cook until the apples are soft and falling apart, about 30 minutes. Remove from heat.
Whisk in mustard, red pepper flakes, and black pepper.
Transfer mixture to blender and puree until completely smooth.
