Ask Mr. Smarty Plants

Glandularia bipinnatifida var. bipinnatifida (Dakota mock vervain) or Prairie verbena is the plant to which you're referring.  Prairie verbena loves disturbed soil!  One of the more noticeable side-effects of clearing cedar (Juniperus ashei (Ashe's juniper)) is soil disturbance which results in drastic changes in flora composition.  Prairie verbena can be seen in great abundance on many pieces of land in the area right now for just that reason.

The best course of action may be no action at all.  Last year, a large, newly-cleared area near Driftwood, Texas was awash in Prairie verbena.  This year, it has all but disappeared as other, more competitive plant species have taken hold there and are pushing it out.

Prairie verbena serves a vital role in habitat restoration often performed by less desirable, more pernicious non-native plant species of holding newly disturbed soil until more permanent species can take hold and become established.  You can think of Prairie verbena as a salve that protects the wounded earth and wears away over time as healing takes place.

If you absolutely have to rid the land of Prairie verbena, hand-pulling is going to be the approach.  Other methods simply disturb the soil even more and slow down the process of regeneration that needs to take place.