I found nothing in the 1851 census, but in the 1861 census there's a Jesse Bryan aged 13, born about 1848 it says, the son of Jesse Bryan and wife Maria. They're living in Burton on Trent in Staffordshire and there are two sisters too, Emma aged 16 and Caroline aged 11. Jesse junior is stated to have been born in Derbyshire.
Jesse senior is a 38 year old slater.
The entry can be found at RG9, Piece 1965, Folio 75, Page 27. Sorry there's no sign of any O'Bryans at all. I checked the original image and it's definitely not a mistranscription - it's quite clearly Jesse Bryan. If these are the right ones and their name is definitely O'Bryan, then it may be that the enumerator wrote the name down wrong and maybe Jesse either couldn't read or didn't notice.
In 1871 there's a Jesse Bryan who appears to be the same one, still living at home with Jesse senior and Maria but by now they live in King's Norton, Worcestershire. Both Jesses are slaters, but Jesse junior is stated to be 32, thus born about 1839. I've checked both images and there's no mistranscription of the ages. If one is wrong, I suspect it's the second one, as the first one where Jesse is only 13, gives no occupation for him.