Buckwheat can be planted during spring and summer in with the veggies. I would plant it among the veggies and use shears to chop it down. I wouldn't bother removing what I chopped either. I would lay it on top of the soil between the plants as a mulch.
The best things about it are that it draws...
Adding to the above lists.....which are great by the way....
buckwheat
clover
cucumbers
And a patch of millet
My soil is awful so buckwheat, clover and millet as cover crops to help my soil and entertain the birds.