A variance in NY is granted by:

Option A is incorrect because the state legislature enacts enabling legislation (such as the Town Law and Village Law) that authorizes municipalities to adopt zoning codes, but it does not grant individual variances — that function is entirely local and administrative, not legislative.

Option C is incorrect because the Governor of New York has no role in local land use decisions or zoning variance proceedings; the Governor's authority is executive and statewide, and intervening in individual zoning cases would violate the separation of powers and the home rule principles embedded in the New York Constitution.

Option D is incorrect because the New York Department of State oversees real estate licensing and certain business regulations but has no jurisdiction over local zoning matters, which are governed by municipal law and administered by locally appointed boards.