1.)First year - don't even try smaller annuals. Go with potatoes and sweet potatoes. Using a pitchfork, plunge it into the woodchips - pry it back and slip a potato in between the ground and the woodchips. The sweet potatoes did especially well.
2.) Bush beans. Just plant them an inch deep into the woodchips. For me, they grew right down through all the wood chips and we had a great harvest.
3.) Big vigorous plants like squash and watermelon.
This brings up another thing in Will Bonsall's book that I never see elsewhere--the difference between old-world and new-world crops. Or actually, between crops from places with the plow and those fromplaces with the digging stick and hoe.
The agriculture of the new world and parts of Africa was swidden cultivation, (used to be called slash and burn). It took place in newly-cleared forest clearings (And even in the places that were not forested, it was on small patches barely cultivated with a digging stick or hoe.) Fire or girdling the trees was used to provide a growing space, and the crops were growing on fungal-dominated forest soils with plenty of duff and twigs and/or wood ash. Soils tended twoard a more acidic ph. After a few years, it was allowed to go back to forest and a new patch was cleared, so there was always a forest soil with tree roots, or a perennial prairie soil with grass roots--not a cropland soil with primarily annuals.
The agriculture of the old world took place in permanent croplands clear-cultivated to a fine tilth with the plow. These received yearly applications of compost/animal manure/ lime and other amendments. Soils tended toward more neutral ph. Crops such as peas and cabbage were the staples. They evolved from maritime beach and riparian plants, which even in nature grow in disturbed soil are then replaced by more aggressive perennials.
So, Bonsall makes the point that on a new homestead, new world crops have an advantage: they have evolved for those fungally-dominated, barely-cultivated, wood-rich soils and will feel right at home. As indeed I experienced on my homestead in Alaska, where I started out new patches of garden by clearing as best I could and planting potatoes, sometimes under nothing but a pile of seaweed.
Mulching with wood chips recreates the swidden garden--fungally-dominated, rich in the breakdown products from wood, and with lots of surface litter.
I wish this distinction had been widely articulated years ago, because it is the rock that many garden methods crash on. They want to have a single method, when plants--in Nature and under our nurture as well--are adapted to different niches.
So the practical application is that tomatoes, squash, beans, and potatoes are happy to live in a bit of soil and a lot of duff, chips, tree roots, half-digested compost, etc. Cabbage, peas, spinach, carrots, lettuce maybe not. They might be happier in later seasons when more decomposition has taken place. Or with the ground cleared of woodchips around them.