My current process as an ASM is:
(1) Video/phone conference with scout to discuss new MB and provide scout with contact info for MBCs I know are currently working with scouts over the 'net (if possible), or who are on the council list (if I don’t already know one working remotely).
(2) I start a new blue card for the scout, sign it, and send a picture to the scout.
(3) The scout is responsible for arranging a tracking method with their MBC, and coordinating with me if they need my support (e.g. connecting the MBC to the scout in Scoutbook).
(4) If the scout completes a badge, the scout is responsible for getting notification from the MBC to me. I accept emails or phone calls from the MBC to log as complete in Scoutbook, assuming the MBC isn’t connected on Scoutbook, plus a counselor-signed blue card in the mail to the scout or to me (to be opened later) if the MBC has them. I have had mixed results getting MBs for scouts without a signed blue card in the past.
My current process as a MBC is:
(1a) If scout already has a blue card, scout sends me a photo of the card.
(1b) If scout is starting the badge new, scout sends me approval “signature” from SM/ASM, and I start a new blue card (I keep several on hand as an ASM).
(2) We meet virtually (phone/video conference) to discuss whatever requirements.
(3) I sign-off either virtually (if my council ever fixes their MBC list) on Scoutbook, or on a hardcopy blue card. I send photos of the signed blue card after each meeting to the scout & parent
(4) I retain the hardcopy blue card until we can meet, unless the scout requests that I send it to them or a leader sooner.