What is this beautiful perennial that has flowers that turn purply pink as it cools? The flowers have rows in an accordion-type shape, for lack of a better term.
On the assumption this plant sprawls and doesn't get very tall (neither growth habit nor foliage is visible in your photo, which would have confirmed a definite ID) it's Oreganum 'Kent Beauty'. It's a prostrate, evergreen sub-shrub which has fragrant leaves - in areas with cool/cold winters, it may not remain evergreen, behaving more like an herbaceous perennial. Despite its being one of the oregano family, it is not usually used for culinary purposes, but grown for its highly decorative and distinctive flower form; the flowers are actually the very small tubular ones (usually mauve/purple or pink) which are surrounded by rose pink bracts. Prefers full sun and free draining soil, especially in winter https://www.shootgardening.co.uk/plant/origanum-kent-beauty
This is Clary Sage (Salvia sclarea). It is only weakly perennial, mostly short lived and best grown as a biennial. The accordion comes from bracts which enclose the salvia type flowers which pale to insignificance from a distance. The leaves are quite different from the bracts; for further identification it might be helpful to show the leaves. Mostly grown for its oil, the plant has a delightful scent, one of my favourites.