Lavender's got a light, floral, and clean-tasting flavor that can go either savory or sweet. Lavender paired with citrus would make a great cookie. Drizzling that cookie with a light icing would make it even better.
Lavender combined with other Provençal herbs like rosemary, basil, thyme, bay leaf, and marjoram would make an awesome base for a savory treat--perhaps even a "Provençal Fields" version of my Scarborough Fair Cookies.
Lavender is a pretty versatile ingredient. (And it doesn't hurt that it's really pretty.) Stay tuned...I'm sure I'll come up with something.