If you have room
I have a little different method I use when I have the room. I have been in situations where the wind is blowing hard enough that I cannot physically pull the boat up the rode. What I do when there is room, is motor in a circle, getting the boat upwind from the anchor, then put the engine in neutral and pull up the anchor as I drift down on it. If it is buried pretty good, I also tend to tie it off to a cleat, and use the engine to break it out. We have mostly mud bottoms here, so I have a marker on the anchor rode, placed so I know it cannot drag back and get the prop. Most of the time I will tie it off, use the engine to break it out, and drag the anchor for a minute or two, which washes off all or most of the mud. This allows me to bring a reasonably clean anchor on board, and to not pile all the sticky mud on deck or into the locker.