I'd serve it over soft, creamy polenta.

If it has the fire of the garlic (I'm just guessing because I make something I would characterize the same way), I would go with some cornbread, and maybe a simple salad with a little fruit (I'm thinking green salad with mandarian oranges/pom seeds/diced apples) and a few pine nuts and a bright dressing. Good luck!

I vote either the pilaf/pasta idea, or the salad idea. I would go either mild or fresh/crisp with your side, since the main dish sound rich and pungent (in a good way).

Is the dish creamy? It sounds delicious!

Grits or polenta and some spinach sauteed with a little onion & balsamic.

A simple pasta tossed with butter, chopped parsley, and grated Parmesan would complement the shrimp.

Lots of good French bread for dipping. Artichoke hearts sauteed in olive oil with lemon. Okra--cornmeal battered and fried. Or sauteed with tomatoes and onions.

Sauteed kale or chard. Rice pilaf or couscous.

A salad with orange and walnuts. Roasted asparagus if you can get it.