The 'inordinate' thing that he is speaking about is the fact that he does not know what Mr. Hyde actually looks like.
And still the figure had no face by which he might know it; even in his dreams, it had no face, or one that baffled him and melted before his eyes; and thus it was that there sprang up and grew apace in the lawyer's mind a singularly strong, almost an inordinate, curiosity to behold the features of the real Mr. Hyde. If he could but once set eyes on him, he thought the mystery would lighten and perhaps roll altogether away, as was the habit of mysterious things when well examined. (2.13)