I have hens so I feed my tegus raw eggs because I know they are really fresh, little chance of salmonilla. I wash the outsides of the eggs with antibacterial soap. the tegus love to carry them around, and learn to neatly poke a hole in the top of the egg so that they can lick out the contents without spilling any of it. It is hilarious to watch.
If I am feeding them questionable or storebought eggs, i like to break it open onto a small dish and microwave it for about 30 secs. so that it is a soft poach with a runny yolk.
One time I fed my blue a cut up hardboiled egg yolk, and I've never seen him have such a hard time trying to swallow something. Got milk? they prefer runny yolks cause they go down easier.