Drawn Butter Sauce is not the same as drawn butter (aka “clarified butter.”) In fact, it doesn’t even use drawn butter.
It’s a light-coloured sauce, made from butter, white wheat flour, water, lemon juice and salt. Fannie Farmer, in her Boston Cooking School cookbook, added a pinch of pepper. If you were to do this, white pepper might be best if available, because then it wouldn’t look like fly specks.
Some restaurants might appear to be confused now. Where you would have at one time been served drawn butter sauce with your lobster, now you might be served just melted butter (not even “drawn aka clarified Butter”), which they’ll say is “drawn butter.” It sounds pricier than melted butter, which, after all, could be just butter left out in a hot restaurant kitchen too long.
A drawn butter sauce is made from 2 parts butter to 1 part flour. You melt 1/2 the butter, whisk in the flour and let it cook a bit (you are making a roux here), but don’t let it brown. Then you whisk in hot (not boiling) water a bit at a time, then cook the sauce over medium-low heat until it thickens, about 5 minutes, and then whisk in lemon juice and salt. Just before serving, add the remaining butter in small pieces, and whisk it in.