Cream butter in a large mixing bowl; gradually add 2 cups sugar, beating well. Add eggs, one at a time, beating well after each addition. Stir in applesauce and spices, mixing well.
Sift together flour, soda, and salt; add to applesauce mixture, stirring just until dry ingredients are moistened. Fold in pecans.
Spoon batter into greased miniature muffin pans, filling two-thirds full. Bake at 350° for 15 minutes. Remove muffins from pans while still warm; sprinkle with powdered sugar. Serve warm.
Note: Batter will keep in refrigerator 1 week.
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