One thing that I'll do when the fingers get cold is to pull the fingers out of the glove fingers and ball them up in a fist and ride the top of the bars (hopefully in a place I won't need to to use the brakes for a while). Usually within a mile or two the fingers are warm enough to put back into the fingers of the gloves, and usually they stay warm enough for the rest of the ride.
I suppose this is the same as using mittens.
Look up "Bar Mitts". They look like a good idea, although I don't have any. Although they do look a bit restrictive.
https://www.google.com/search?q=Bar+Mitts&oq=Bar+Mitts