Is Self-plagiarism allowed in two submitted articles by one author?
If the method is taken from elsewhere you should cite the protocol, and use block quote if necessary. If the method is novel, then pay attention during the submission, you should see one common question asking if the work has been presented or circulated elsewhere, you may use that to declare the potential repetition and let the editors decide. If no such slot exists, it's better to inform the editor in the cover letter.

Moving forward, consider cascading your publications: while paper A is under review, paper B should be being finalized, paper C being drafted, paper D's experiment being done, paper E and on being conceptualized. That way you can avoid problem like such and still maintain a reasonable output level.

To be honest, if I saw two papers from the same author saying "education data were broken down into 3 levels: less than high school, high school completed, and college or above." I will not jump off my chair and scream "plagiarism!!" But people's ideas about this issue are not all the same, I'd agree that assuming the worst would be a good approach.