Hampshire Sheen Danish Oil is one of my go to finishes for food-safe bowls with brilliant results.  With more coats and light sanding inbetween using 2,000 grit or higher wet/dry paper you will achieve a glassy finish.
 
Hampshire Sheen’s Danish Oil is food safe and compliant to EN71 toy safe when dry. Thinner, more penetrating and less smelly that other Danish Oils, this product contains only pure Tung Oil and no artificial varnish, resins or other vegetable oils.

The solvent used to aid drying is dearomatised white spirit, which is less irritating to skin and lower in odour than traditional white spirit, and is completely biodegradable. Easy to apply; more than 50% Tung Oil; Food and Toy Safe (and odourless) when dry; Deeply penetrating and protecting: Will not chip, flake or peel; Naturally water resistant.

Supplied in 500ml lacquered tin cone bottles and double sealed.
 
Important: Make sure to dispose of the application rag/tissue in a fireplace.  There is a slight danger of spontaneous combustion when using Danish Oil due to the heat generated while the product cures.
 
This product may not be compliant with food and toy safe regulations outside the EU.