It's the writer's impression of the little Italian "nonna". They are famous for good home cooking, so the writer expected that this bossy little old Italian woman probably spent a lot of time cooking for the family as well, and disciplined unruly kids with a handy wooden spoon.

In the United States, in order to discipline children, parents used to hit them. Wooden spoons were one of a number of objects that were traditionally used for this purpose. Others included: slippers, belts, hairbrushes, and rulers. "She looked like she would've smacked me with a wooden spoon, if she'd had one" means "the same kind of anger a parent might express toward a disobedient child."

that 's very helpful！！！"anger" is an noun ，“angry ”is a adj. right? thanks very much!

Here is a suggestion about the wording of your question: I wonder IF it is an expression to show ANGER, and why? OR I wonder WHETHER OR NOT it is an expression to show ANGER,and why?