Toss the sweet potato pieces in a small amount of oil, or use oil spray, and bake in the oven in a casserole dish for 30 minutes or until fork tender.
Mix spices. While the sweet potatoes are cooking, mix the ¼ cup of brown sugar, cinnamon, nutmeg, allspice, and salt in a small bowl.
Make topping. In a separate larger bowl, mix the pecans, flour, butter/margarine, and the other ¼ cup of brown sugar. It helps to use your hand to rub the ingredients together between your fingers, as the butter may stay clumped up and not mix well with just a spoon.
Add apples. Once the sweet potatoes are done, add the apples to the casserole dish and mix until fairly evenly distributed. Then sprinkle over the sugar and spice mix.
Top with the crumble mix as evenly as possible, then put in the oven for 30 minutes until the topping is golden-brown and has a nice crunch.