High-handedly is how you talk about the *way* someone uses their power, not the kind of person they are. If a manager high-handedly cancels the meeting, they did it from above, without asking, as if other people’s time did not count. Same idea as high-handed — using authority in an unreasonable way — but stuck onto the verb. It still sounds a little formal, and it still never means something good. You will hear it in news and in complaints more than at the dinner table.