There are a few lavenders in my garden, all look familiar and produce
what - superficially anyway - appear to be identical looking flowers
but a couple of them seem to tolerate, even thrive on, pruning well
back behind the leaf into the woody stem and producing new growth.
Their leaves (the prunable ones) also have a more lush and dense
greener leaf distinct from the tall grey rabbit-ear leaf of what I
take to be the more common lavender.

Could someone help me to identify these?

Can you post a picture?