There are tonnes of theories about about how Caravaggio underpainted his paintings. Below is a PhotoShop version of one of the many—each based on the available evidence—but MJA thinks that this is the most likely one. It’s certainly efficient. (Click on the image for a larger version.)
Essentially, this method comprises a three- or four-tone golden-brown field-colour underpainting onto which the main elements (the people) are worked up en grisaille, using black-&-white greys. This produces a very light base and cool, bluish transition tones onto which the semi-opaque, semi-transparent local flesh colours are broadly painted. This light grey underpainting causes the overpainting colours to glow, in a way that direct painting cannot match, and its “blueness” counteracts to a large degree the browning of the oils as the painting dries over the years.