You seem to have some good information on your ancestors.
I think Bruflat is in Telemark fylke in the south of Norway.
But at familysearch.org I found that someone has submitted genealogy for this family, and has Bruflat Oppland Norway.
so I could be wrong.
go to this pagehttp://www.familysearch.org/Eng/Search/frameset_search.asp
type in Ole Espeseth
and you will see ancestral files for Ole Espeseth - click on that and then scroll down and click on Submitter Details. Then you will see the address of the submitter.
She has Dalyville Wisconsin for the younger Ole's burial, but also has his father in Wisconsin too? But the mother Gertru Arnesdatter, who seemed to live longer she has dying in Norway. Hmmm.
Ole Espeseth can be found on the 1880 census - search here, his wife seems to have Americanized her name to Esther (or the census taker did)http://www.familysearch.org/Eng/Search/frameset_search.asp?P...
It has him born 1848 in Norway. Living in Maple Grove Township, Barron Co. Wisc.
There were nine with the last name Espeseth or close spelling to that living in Barron Co. wisconsin. Perhaps other relatives who had come from Norway? The son Gilbert was born there in 1879? Perhaps there is a birth record for him or a church record?
1508 Arne Espeseth m 66 stone mason N N N 136 Cumberland Barron Co.
1992 Ary Espeseth m 28 f N N N 155 Dallas Barron Co.
1993 Knudt Espeseth m 22 bro Wis N N 155 Dallas Barron Co.
1994 Julia Espeseth f 19 sis Wis N N 155 Dallas Barron Co.
2263 Ole Espeseth m 32 f N N N 164 Maple Grove Barron Co.
2264 Esther Espeseth f 27 N N N 164 Maple Grove Barron Co.
2265 Ole Espeseth m 6 Wis N N 164 Maple Grove Barron Co.
2266 Gilbert Espeseth m 7/12 Dec Wis N N 164 Maple Grove Barron Co.
23303 Halver Espeset m 24 lab N N N 362 Vermont Dane Co.
The descendants also seem to be posted for the sons Ole and Gilbert and their sister Ida born later.
The info on that LDS familysearch.org site is not always accurate - just what someone posted from their own research - and sometimes some extrapolation. But it might be someone to contact.