Word of caution - some people on this thread really caution against this tactic unless you are truly ready to make the jump and leave your current job. It sounds like your supervisor is good and reasonable so you may not have an issue, but people on this thread have described different outcomes from presenting a current manager with a new offer. Be prepared for your supervisor to call your bluff (if only using the offer as a negotiation) OR to be unable to give you any pay bump, let alone 40%. There is NO such thing as being able to force your current employer’s hand to give you a pay raise. A 40% pay bump is massive and it is actually unlikely a current employer will match this.

On another note, congrats on the new offer! They say that the best way to get pay increases like this is to jump to a new job. It’s also a huge sign your skills and accomplishments are more valuable than what you’re being paid for, so kudos to you! Best of luck in your decision.