Not razor sharp..I have the same lens and love it. I find that F8-F11 are best for a setup like this. And if you want to really black out the background. Keep the subject and the background as far away from each other as you can. Dial your aperture down to the smallest opening F25/F29 depending on you focal length. Put as much light on the subject as you can while keeping off the background. This will let the shutter open and close before the light has a chance to reflect off the background and back into the camera. More light would have helped the color of the pepper POP too.
I like the composition, the subject, and overall idea (I shot something very similar)here. Please PM me if you have any questions or comments
The problem here isn't the not-all-black background (actually, I like how the bowl and the background are still separated), it is the shallow DOF - many viewers don't like it, when the frontmost parts are OOF – and the long exposure, that made the flame look kinda strange. In addition, it is clearly visible, that the flame comes from behind the chili.
Not sure what you used for your background , however a good way to get a really black background is to use black velvet.
Another way would be to post process using Photoshop CS3 , go to Image > adjust > selective color. Choose the black slider & move it to the right. That should blacken your background further