People are starting to get used to the idea that the hebes and parahebes of New Zealand really do belong back in the genus Veronica, where they were first classified by Forster after Cook's second voyage. Our 120+ species of shrubby hebes, subshrubby speedwell hebes & sun hebes, and cushion plant snow hebes are an amazing group of plants that have diverged from the standard northern veronicas in many different ways. They're classified now as Veronica section Hebe, and their sister group (with a shared ancestor in common) is the Australian Veronica sect. Labiatoides.
Diggers' speedwell is one of these Australian veronicas (Veronica perfoliata). It grows in south-eastern Australia and it's occasionally cultivated in New Zealand. This rather straggly plant has been growing in a pot, but given a good spot in the garden it will adopt a nice rounded form from a bunch of new shoots that arise from the rootstock each spring. The leaves are very Eucalyptus-like, bluish green and very firm, and joined in opposite pairs to surround the stem—that's what perfoliate means. In fact if you saw it when not in flower, you'd probably think it was a gum tree seedling.
The flowers are a strong mauve colour, with a little pink surrounding a dense tuft of glassy hairs in the centre. These long glassy hairs are found in quite a few of the Australian species (like V. derwentiana and V. nivea), but we don't see anything like them in New Zealand Veronica. It's easy to propagate from cuttings. You can cut the stem up just above every pair of leaves, so each internode makes a good cutting.
Just as our veronicas have evolved away from the northern type here in New Zealand, so have their relatives in Australia. The similarity to a eucalypt isn't an accident; such sclerophyllous leaves are adaptive in the Australian environment and common in many unrelated plant groups.