Did you make these muffins in Home Ec?? It's been around awhile, and with good reason because holy cow you dip the entire muffin in butter and then roll it in cinnamon sugar. According to Betty Crocker, they are called French Breakfast Puffs. (I think somebody in their test kitchen was feelin' fancy)
Grease a muffin tin with butter or nonstick spray (we're making 10 muffins)
In a large bowl or stand mixer, beat 1/3 cup butter until smooth. (I use the measurement on the wrapper to see where 1/3 cup is.)
Beat in 1/2 cup sugar until fluffy.
Add 1 egg and beat until smooth.
Add 1 cup flour, baking powder, salt, and nutmeg, but don't stir. Use a small spoon to stir the dry ingredients together, and then gently beat the dry ingredients into the wet.
Before the flour is fully incorporated, add the milk. Beat until almost incorporated.
Add the 1/2 cup of flour. Beat very gently (or use a spoon) to mix until everything has just barely come together.
Use a spoon or small measuring cup to divide the batter between 10 greased muffin tins.
Bake the muffins on the center rack for about 20-23 minutes. The tops of the muffins will just barely start to be golden when they are done. You can also insert a toothpick into the center of a muffin, and if it comes out dry, then they are done.
When the muffins have cooled for a couple minutes, use a knife to release the muffins from the pan. Remove to a cooling rack.
Melt 1/2 cup butter in a small bowl. In another small bowl, stir together 1/2 cup sugar and 2-3 teaspoons cinnamon (to taste).
When the muffins are cool enough to handle but still hot, dip each one in the butter (all of it! Top and bottom!) and then roll it in the cinnamon sugar. Some people say you should just dip the tops of the muffins. Those people are wrong.
Eat hot! Share!
Notes
You can totally make these in a mini muffin pan. I would guess it would make between 20-24 mini muffins. You will have to take a guess on the baking time, it will definitely be less time, start with 10 minutes. They are done when they are golden on top.