Answer: Too bad we aren't like sheep that can eat pretty much whatever grows in front of them! I suggest that you put down a thick layer of newspaper (3-5 sheets deep) over the grass followed by a thick layer (2-3") of old hay. New hay may introduce more unwanted seed to your garden - old hay will have fewer seeds. Clip or mow the grass as close to your crop plants as possible before applying the mulch. If grass starts to grow through at any point, throw down some more of the mulch combination.
To control the grass for next year, lay something over the mulched beds to further smother the grass (corrugated cardboard, old planks, plastic or tarps). Do this as soon as you've removed all crop debris in the fall. The sooner you can start this, the better. Next spring remove the covers and till only the areas you will plant, leaving the rest of the mulch in place. Best of luck!
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