Cuban Thyme/Cuban Oregano. The will to live is strong.
Last year, I bought one of these, and at the end of the season, I just didn't want to try to winter it over, not enough space in the house and they're cheap.
So, I cut it off at the soil line, and hung the entire thing to dry for cooking.
Which was a mistake. Being so succulent, it didn't dry. It sat there and slowly grew new growth from the terminal ends, and slowly shriveled a bit as it used stored water from its tissue.
Finally, I felt sorry enough for it that I took a couple of cuttings and threw them in water. One grew roots, the rest rotted. I'm going to plant the new one out this weekend.
The rest, to dry it, I had to finally strip the leaves and put on a cookie sheet in a 170 degree oven for about 6 hours. I've been using that all winter to cook with, wonderful flavor.
If you haven't tried this herb, give it a whirl. It's fun and easy to grow, and a good ornamental in combo planters for the summer.
http://en.wikipedia.org/wiki/Plectranthus_amboinicus
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outside without fuss and comes back hearty every Spring. Amazing little plant. 
"tender perennial" so it will come inside for the winter. It's a little spicier than regular basil with much smaller leaves. So far, it's a winner.
