Verified answer

You can spin the egg. Since viscosity is a measure of a liquid's resistance to shear forces, seeing how the egg resists spinning (or continues to spin after you stop it) will tell you something about its viscosity. A thin yolk will continue to spin after you stop it because the inner yolk continues to spin even though the outer layers are stopped. As the inner yolk spins, it applies a shear force to the outer layers, which eventually cause the egg to spin again. A very viscous yolk (say, a hard boiled egg) resists shearing altogether, and the inner yolk stops when you stop it, so there is no spinning afterwards.

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You can't. There's an olld saying that applies here.."you can't make an omelet wihout breaking a few eggs."