Its Perovskia atriplicifolia, probably Perovskia a. 'Blue Spire'. Classed as a sub shrub, behaves like an herbaceous perennial, Cut to the ground in late autumn - it'll grow again next year. It has the common name of Russian Sage, but it is not related directly to sage, and should not be eaten, cooked or otherwise.

We find that it suckers rather extensively here.

I wouldn't encourage in the garden!

Although I do not recommend eating it, Perovskia species are members of the Lamiaceæ, along with sage (Salvia), so Russian Sage is a reasonable enough name. Perovskia is classed in the same subfamily, Nepetoideæ, and even the same tribe as Salvia, Mentheæ (mint-like Lamiaceæ).

Many other culinary herbs also belong to the Lamiaceæ.

I've planted loads of these in different gardens over the years, including my own, and never had a problem with them getting out of hand - they're a very useful, later and long flowering addition to a border or bed, and a good contrast to all the yellow and orange flowered plants that are starting or will shortly be in flower.

Good for wildlife too I think.