There aren’t many invasive exotic plants that I like, but count Brazilian vervain (Verbena brasiliensis) as one of them. It is widespread in our old fields, but it doesn’t seem to establish to the exclusion of other species. Plus Will Cook says its a decent butterfly attractor and we find it to be a nice bouquet filler in the fall with its strong green stems and subtle purple flowers.
One surprising thing of note about this Brazilian plant is that it seems to leaf out more in the winter than the summer. Does anyone know from what part of Brazil this plant originates? Maybe a more temperate climate?