My personal method is based on my experience with IFS therapy/parts work, but truthfully I don't know if this will work for anyone but me. Still, I've had success with the following:

I envision the younger version of me that did the embarrassing thing. In my head, I see the current, adult version of myself talking to the younger one. I explain to my younger self that I don't find them shameful, that I understand why they acted the way they did, and that I forgive them for everything. I listen as the younger version brings up any additional concerns and offer any further reassurance/comfort/love that I wish to. It's important to take time with this and really sit with the uncomfortable feelings.

For me, this can resolve the acute shame feeling, and also prevent the memory from coming up again suddenly, or at least from hurting as much when it does.