Prep: Preheat the oven to 350F. Line a 8 or 9” square pan or cake tin with parchment paper or grease generously.
Make the Crumble: Mix the melted butter, flour, sugar, cinnamon, and salt together in a small bowl. Set aside.
Dry Ingredients: Whisk the flour, baking powder, baking soda, cinnamon, ginger, nutmeg,and salt together in a large bowl. Create a well in the center of the bowl.
Wet Ingredients: Add the melted oil or butter, sugar, applesauce, apple cider vinegar, and vanilla to the center of the bowl and slowly incorporate it into the dry ingredients until a thick dough forms. Add the carrots and pecans to the batter and fold in, until evenly distributed.
Assemble: Transfer the batter to the baking pan and use a spatula to spread it evenly across the base. Then, use your hands to evenly “crumble” the crumble over the batter.
Bake: Bake in the middle rack of the oven for 30-35 minutes, or until a toothpick comes out of the center of the cake cleanly. Set aside and let cool for at least 10 minutes before slicing.
Serve & Store: Serve warm, or let cool completely before serving. Store leftovers at room temperature for up to 3 days, in the fridge for up to a week, or in the freezer for up to 2 months.