Can you paint hard cardboard with varnish?

Yes, as long as you gesso it first. Gesso is a white acrylic paint you can get at any craft or art store. Without Gesso, the cardboard will absorb much more of the oil paint and will peel and crack faster. Gessoing will save you money on oil paint and touch-ups! To gesso, take a large brush and a dish of water. Paint the cardboard with a thin layer of the gesso, thinning it out with the water. Make sure all your strokes go in one direction. After you've done one thin coat, let it dry. Then do another one, only with the strokes in the other direction. After that layer has dried, do a last coat in the original stroke direction. Remember to let the gesso dry completely before starting to paint with oil paints!