Generally, an employee isn't bound to any requirements about how much advance notice is to be given. Iowa is an at-will employment state, which means as a general proposition that either employer or employee can end the relationship at any time. There are exceptions, of course. For example, if your employer paid for certain training for you, you might be obligated to work for a certain period or be liable to repay some of the cost. Consult an attorney if you have any concerns along that line, but if your only concern arises from the handbook, then I don't think you are restricted. Your employer should be glad you gave 2-week's notice.
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I think that your employer is incorrect. In an at-will employee state, you have the right to quit at any time and they can't force you to provide a longer notice. You didn't even need to necessarily provide the 2-week notice. You should feel free to go ahead and take the new job
The information provided in this answer does not create an attorney-client relationship and is not considered to be legal advice.