You probably don't have enough mint in the garden for the sauce now, and the leaves will be very small and fiddly. So I would buy some from a supermarket. It is interesting that some think that balsamic vinegar is good in mint sauce, and others not. I personally think that balsamic is too heavy for mint sauce, but it's personal taste. I like to use cider vinegar which I think a little lighter than classic malt vinegar.
This is our family recipe: Every late summer, gather lots of mint (I grow in tubs which I change on alternate years) chop fairly finely, but to taste, and store in a screwtop jar with enough vinegar to cover. When wanted, take out a few spoonsful, add a little sugar, and more vinegar to taste. Any left over can go back in the jar.
I think that the boiling water is to soften the leaves, but our family thinks that they are fine as they are. And I always make it for French friends - I think it so unlike any of their classic sauces which is why they like it.
Enjoy your roast dinner! Oh, and if you buy ones of those pots with the mint in, bung it in a tub afterwards.