A phone call from a prospective employer is not a job offer. Proper HR departments know full well that to recruit staff they need to work around prospective candidates working hours. Phone calls that don't leave messages are most likely time wasters or dodgy recruitment agencies. Wait until you go on a few interviews and get a few proper job offers before you give notice. Imagine the pressure once you've left your current job with no other job lined up and are sitting at home. You'll become more stressed worrying about job interviews because they will be more intense because you are now desperate for work. This may make your stutter worse and bring down your self-esteem, creating a negative feedback loop. And this will not be unnoticed by perspective employers. Contrast that with looking for work while employed. You can pick and choose from job offers and employers will be more in to you because you are currently employed and valued by another employer. Don't throw that advantage away.