Yep, raised bed(s) is the answer. Just be sure to have it high enough so that you have at least 12" of rich, organic, soil above the natural soil-line. Personally, I would shoot for a 16" depth. Most vegetables and herbs are referred to as "shallow-rooted" plants. For deep-rooted vegetables such as potatoes (both Irish and sweet), some, but not all radishes, most carrots, and some but not all onions, I would go for 20" (or more) depth. All things being equal, the deeper the "good" soil the better.
You can even build a raised bed on top of a raised bed, as this picture shows, using 1x6" to 2-12" treated lumber. This gives additional depth without having the entire bed so deep. This bed-on-bed is also useful if your raised bed is in an area that does not drain well or is in a valley, holding water too long. This picture was taken in late summer and you see asparagus, sweet potatoes, peppers, onions and gourmet garlic. The bed-on-beds are used for the garlic, since this entire (primary) raised bed was built at the bottom of a slope. I wanted to increase the drainage.
