There are various ways of introducing wax to wood, including dissolving the wax into the mineral oil (this makes what some call "board butter" or "spoon butter"), making up a conventional paste wax, or by applying it molten.
The goal here is to get the wax to be absorbed by the wood as deeply as possible, not just to apply a coat of wax to the surface which is then buffed to a shine as is normally done on furniture. To best facilitate this the wax needs to made liquid.
IMO melting the wax* and applying it to directly to the wood is by far the best option for an end-grain board.
Regardless of whether you use a "board butter" or apply straight melted wax I think you should warm the wood before application so that it doesn't begin to set the moment it touches the surface. You will generally get much deeper penetration this way.
A heat gun can be used to pre-heat the board if handled with care, but a normal hairdryer will put out sufficient heat. Since the wood will cool off fairly quickly on its own it's best to do this one area at a time, so you'll work over the board section by section.
How to apply
Couldn't be simpler, you just dip a brush into the wax and start brushing it onto the pre-warmed surface.
When you're done and all the wax has cooled and solidified some excess will need to be removed from the surface and scraping is probably the most efficient method. You can use the edge of a kitchen knife for this if you don't own any conventional wood scrapers. For the grooved areas a spoon will work great, its edge can be sharpened if necessary but remember to blunt it afterwards if you return it to normal duties!
*Unless you have a low-temperature heat source like a hotplate it's best to melt the wax in a double boiler (simplest version is a glass, ceramic or metal bowl suspended in simmering water). Once fully molten the wax will have become clear.