Preheat oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking pan.
Whisk flour, baking powder, cinnamon, ginger, nutmeg, salt, and cloves together in a bowl.
Beat oil, applesauce, brown sugar, white sugar, and orange juice together in a separate bowl using an electric mixer until smooth. Beat eggs, 1 at a time, into applesauce mixture, beating until each egg is fully incorporated before adding next egg.
Mix flour mixture into applesauce mixture, alternating with carrots, walnuts, and jalapeno pepper, until batter is just blended; pour into prepared baking pan.
Bake in the preheated oven until a toothpick inserted in the center of the cake comes out clean, about 50 minutes.