That little hole in the handle of your pots and pans was made to hold a spoon or other stirring utensil!
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I use the top from a margarine tub for a spoon rest. It is big enough to catch the drips. It is easy to wash! It keeps the stove top clean.
I drink a lot of tea and coffee during the day. To kill a tree for wooden, or waste plastic for stirrers is not on my list of "smart things to do". Neither, is washing spoons all day or wasting space on my tiny "coffee spotted" counters.
When using a long spoon for stirring soup, etc., I rest the spoon in a coffee cup. It takes up less space and makes less mess on the stove.
My family goes through a lot of sliced cheese. I kept throwing away those little clear plastic wrappers from the slices and wondering what else could be done with them. I finally found something they're good for - they make excellent disposable spoon rests!