Preheat oven to 400 degrees F and prepare the muffin tray by treating it with non-stick cooking spray or use lining cups with cupcake papers.
Pulse the hazelnuts in a food processor until they are ground and then add all of the dry ingredients, including the spices, to the food processor and pulse until everything is well mixed. Add the remaining ingredients, except for the jam, and process to mix. (If you are using a mixer, cream the egg, applesauce, and sugars. Then mix in the milk and vanilla, add the dry ingredients and lemon peel, and fold in the nuts.)
To bake, spoon a tablespoon of batter into each of the 12 muffin sections and then top the batter with a tablespoon of seedless black raspberry jam per muffin. Evenly divide the remaining muffin batter between the 12 muffins, using it to top the jam. Gently spread the batter to cover the jam and then bake for 15 to 20 minutes, or until lightly browned.