Tempera grassa was a common painting medium in the 15th century. Since then, not so much (though with a few notable exceptions). It's an interesting medium to work with.
Tempera grassa is an emulsion of egg and oil (an emulsion is a liquid in which tiny drops of another liquid are suspended). Egg yolk is a natural emulsion that incorporates oil into its makeup fairly easily. You are already familiar with an egg-oil emulsion—it’s called mayonnaise. Tempera grassa is essentially mayonnaise made with a drying oil such as linseed or walnut.
To make a simple kind of tempera grassa, separate an egg yolk and put it into a small cup. Measure the volume of yolk, then measure out the desired volume of oil. Add just a few of drops of oil to the egg, mixing thoroughly as you do so. Add a little more oil and continue mixing. Repeat, adding oil a few drops at a time, until all of it has been blended in.
The amount of oil to use will depend on your preference; anywhere from a few drops to an amount equal to half again the amount of egg will work. The more oil, the more slowly the paint will dry and the more it will handle like oil paint. If you are just starting, try five parts egg to three parts oil (which produces a moderately egg-rich mixture). If you’ve worked with egg tempera, an egg-rich formula will handle in a familiar way. Once you have mixed the egg and oil into an emulsion, you will want to add some water, blending it in a few drops at a time in the same manner that you added the oil. I have had good results with a mixture of 5 parts egg to 3 parts oil and 1.5 parts water, but you should feel free to experiment.
This substance is your painting medium. It will keep in the refrigerator for a week or so, depending on how much oil it contains (throw it away and clean the container thoroughly if it starts to smell). Mix in a couple of drops of water before each day’s session to compensate for evaporation. You can make paint with it by mixing together approximately equal amounts of medium and a paste of pigment and water. You can thin the paint with any desired amount of water; the important ratio is that of medium to pigment.
Raw pigment powder is available in some larger art stores and from places like www.sinopia.com. Prepare it by putting the powder into a small jar, adding distilled water, and shaking. Wear a dust mask when working with pigment powders.
Some artists use tube watercolor or gouache paint instead of pigment for egg tempera and tempera grassa. I haven't tried that (you may have noticed that I'm kind of a purist with these things), but I don't see any reason why it wouldn't work.
It is important get the ratio of pigment to binding medium right with tempera grassa. Practice on test pieces until you can consistently make acceptable paint. Tempera grassa paint made with too little medium will feel powdery once it dries. You can correct this by painting over it with thinned medium or with thinned egg yolk. Tempera grassa paint made with too much medium is difficult to work with and dries poorly. After the water and egg dry, it will have a crumbly, sticky feel if you run your hand over the surface. Don’t paint additional layers over it in this state, as you will probably get poor adhesion. You can either wait for the oil component of the paint to harden, which can take a day or two (or more with an oil-rich formula), or you can carefully scrape the paint off with a knife and start over. It is also true that tempera grassa mixtures very occasionally fail to form stable emulsions, becoming gummy and unworkable. The paint will then refuse to dry for very extended periods (up to a couple of weeks). I don’t know why this occurs; I’ve had this happen only a couple of times. If the medium seems intractable or the oil and egg combine incompletely, throw it away, scrape off any paint you may have applied, and start over.