Les,
Always happy to try and help. This was a really knotty piece with lots of inclusions running right through the piece.
The first coats of Danish Oil were brushed on and brushed well into the inclusions. Fine, except that this caused runs on the read of the bowl. Had to power sand these off.
The next coats were put on fairly sparingly with paper and some extra just lightly brushed into the inclusions.
I gave the bowl a light de-nib with Webrax between coats and buffed up with a clean soft cloth. Each coat had any excess wiped off after about 20 mins and then left to dry overnight. Final buffing was with a Chestnut Buffing System wheel C or use any soft wheel you have in the shop.
I think the piece had about 6 coats in all.
You can also try using EEE-Ultrashine which gives a high gloss wax finish - works well on Birch.
This way worked for me but do experiment and see what gives the best results for you.
Best of luck and look forward to seeing a photo!
David