I'd leave it there and use it to suppress weed growth.

Agree. Assuming your garden layout is semi-permanent just rake back the straw, punch a hole in the paper and plant. No need to remove it just layer new mulch on top.

If, on the other hand you must till/rearrange/etc. the bed then just till it in. Be sure to add additional N fertilizer of some kind to compensate for the tilled in carbons.

Dave

I assume you have a compost bin then you could add last years mulch to your bin and start this year with fresh straw.

Thanks to you all. Dave, I think you answered my chief concern ie. how to compensate for all that undigested carbon. My vegs are in 4'x 8' raised beds. What would be a suitable amount of nitrogen (and in what form)?