There are a handful of reasons why muffins turn out dry. The most common reasons are overbaking and overworking the batter. In cases of overbaking, you can check first the level of dryness.
If the muffins are dry on the inside, use a technique called the wet glaze. All you have to do is soak some icing sugar in milk. Then, using a toothpick, prick some holes into the muffin and start brushing it with the wet glaze.
On the other hand, in cases of overworked muffin batter, all you have to do is adjust the dough. For instance, adding more flour will be the immediate solution to a sticky batter.
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