Turn the oven on and set the heat to 350 degrees. Put cupcake liners in 12 cupcake or muffin cups.
Put the sugar and eggs in the large bowl. Beat with the spoon until the mixture is evenly blended.
Add the applesauce and oil and mix well.
Add the flour and sprinkle the salt, cinnamon, and baking soda evenly over the flour. Mix well.
Use a 1/3-cup measure to fill each of the lined muffin cups 3⁄4 of the way to the top.
Put the muffin tin in the oven and bake until the muffin tops are slightly browned and rounded, and a toothpick, stuck into the middle and pulled out again, comes out clean, about 25 minutes.
Let sit until cool, about 15 minutes. Then remove the cupcakes from the tins.
Put the cream cheese in the small bowl and, using the fork, mash until creamy.
Add the yogurt and mash again.
Add the honey and mix well. Cover and refrigerate at least 1 hour and up to overnight.
Use the butter knife to spread the icing on the cupcakes. Or, if you want toget fancy, put the icing in the bag and snip off a tiny corner (the smaller the hole, the finer the line). Push the icing toward the hole. Squeeze the bag gently and pipe the icing onto the cooled cupcake in concentric circles. Serve right away (the icing won’t keep well).