Need advice converting grass lawn to vedgie garden.

My little lady and I finally got out of apartment living to buy a little condo with about 500 square feet of grass that we'd like to turn into a vedgie garden. So.. .I went out and got a shovel, a hoe and a pickaxe. We weeded out what wasn't grass and set to work breaking up the sod.
Now, we live in Hawaii so the sod is thick, thick, thick. So thick, in fact, when I pull a chunk out and examine the cross-section, it's hard to decide where grass+air ends and roots+soil starts. It's coming up like carpet.
How do I break this up to be ready for vedgies?
Thanks in advance.
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snipped-for-privacy@telling.com wrote:

First, I'm looking it up.... hmm.... "Envy...." Yep, still on the list!
Ask the local garden types; my guess is that you get rid of sod the same way we do in the frigid zones if we're feeling lazy. Put down a barrier of something like newspaper, and top with all the mulch material you can lay your hands on. I have done that in the fall and rototilled in the spring, and the grass had pretty much rotted away. Of course, you don't have spring, really, which is balanced somewhat by not having fall and winter.
BTW, I saw an asparagus growing operation on Maui where they let the tops grow for a while, then mowed them down and started harvesting the spears. Rotated around the bed, so some were producing and others recovering.
I've got enough miles on the credit card; I think a couple of weeks on Kauai'i in the land of Hanalei will work...
Peace,
Gary Woods AKA K2AHC- PGP key on request, or at www.albany.net/~gwoods Zone 5/6 in upstate New York, 1200' elevation. NY WO G
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