Details on the constitutional provisions on the reconvened session are here.
To override the Governor’s veto requires the vote of three-fifths of the members present and voting. Article II, Section 22(1) of the North Carolina Constitution states in part:
If the Governor approves, the Governor shall sign it and it shall become a law; but if not, the Governor shall return it with objections, together with a veto message stating the reasons for such objections, to that house in which it shall have originated, which shall enter the objections and veto message at large on its journal, and proceed to reconsider it. If after such reconsideration three-fifths of the members of that house present and voting shall agree to pass the bill, it shall be sent, together with the objections and veto message, to the other house, by which it shall likewise be reconsidered; and if approved by three-fifths of the members of that house present and voting, it shall become a law notwithstanding the objections of the Governor. In all such cases the votes of both houses shall be determined by yeas and nays, and the names of the members voting shall be entered on the journal of each house respectively.
Since the veto was given to the Governor by constitutional amendment by the voters in 1996, no veto has been overridden. Post-colonial history of action on gubernatorial vetoes is linked here. No other business may be transacted other than an adjournment resolution.
*I’m posting from the Mountain Time Zone