Preheat oven to 350F. Line the muffin tin with liners. Mix almonds and jaggery for the crumb topping. Set aside.
Mix flour, baking powder, baking soda, salt, cinnamon and allspice in a bowl. In a different bowl, cream butter, jaggery and applesauce together, until light and fluffy. Add eggs, one at a time, mixing well after each addition. Add vanilla extract. Mix in flour alternating with milk. Finally, fold in pears and chestnuts. Take care not to over mix the batter.
Scoop the batter onto the cupcake liners, top with the crumb topping and bake for about 25 minutes for large muffins or 20 minutes for standard size muffins. Test doneness by inserting a clean knife into the muffin. They should come clean. Take the muffins out, cool on a wire rack. Serve warm with coffee or ice cream.