You might try low growing clover. I dont think it spreads from the roots. It also fixes airbourn nitrogen into the soil.

I'm pretty sure clover spreads by it's roots and very aggressively at that. It's also a very potent seed spreader. There may be a differant hybrid out there that will fit the bill, though.
This doesn't seem to be and easy solution.
Would mulch and stepping stones be a better way to go. Or maybe stepping stones with Irish moss growing around them?
I hope it all works out.

Hi Sweetbrat,

All the clovers I know of spread, some of them invasively, so be really careful if you decide to go that way.

Being a vegetable garden, I assume this is a very sunny spot!!? You might want to try one of the creeping thymes, Thymus praecox. They only get a couple inches high, have tiny, tiny leaves, and have tiny flowers that range from white to light pink to deep pink. The one I like best is T.p. 'Coccineus', Red Mother of Thyme with bright rosy-pink flowers.They can tolerate some foot traffic, but not constantly. The toughest one, the one that will tolerate the most foot traffic, is T.p. 'Pseudolanuginosus', Woolly Thyme. It has lavender-pink flowers and the tiny leaves are kind of fuzzy. The foliage is grayer than the others. If there are places where you walk often, as I suspect you must do when tending the vegetables, I'd suggest you put fairly widely spaced stepping stones in and plant the thymes all around and between them. Creeping thyme is one of the most popular "patio stuffers," used by a lot of people to plant between bricks or stones on patios and walkways. It will start to grow over the stones and you can either leave it go or trim it back if you like the look better. Compared to mowing and trimming grass, it will require very little upkeep. You might want to shear the top off after it's done blooming to keep it neat looking, and possibly another time or two over summer. If you decide to do it, rather than getting a few big plants and spacing them far apart, they will usually grow together faster if you get small plants (2" pots should work well) and space them closer together. Be sure you get all the grass and any weeds out before you plant since it will be much harder to weed out after the thyme is in and spreading. Thyme spreads only on the surface and is very controllable.

Happy veggie gardening,
Skybird