The only company I’ve found that does produce large left- and right-handed palettes is Richeson, in wood and melamine (Buy Direct). Their ‘normal’ melamine palette has a neoprene thumb insert, which means it’s suitable for holding in either hand.
If you know a woodworker, or are handy yourself, you could make one fairly easily using a piece of marine ply. Borrow a palette from a right-handed friend to trace the shape, cut out the shape and then a thumb hole in the relevant spot for holding it. (You want the bulk of the palette to be on the “far” side of your arm, away from your body.) Sand and oil with whatever oil you use as a medium. It’s worth taking the time to chamfer the edge of the hole as it does make it easier on your hand if you do a lot of painting.
A basic wooden one where the thumb hole hasn’t been chamfered (cut at an angle) could be flipped over and used by a left-handed artist (that is, palette held in your right hand, brushes in your left). Though you might want to take some sandpaper to it yourself to smooth down the edge if you’re going to be holding it for extended periods.