Evenly sauteing green beans

Try blanching them first, that way they will be almost cooked before you start frying them. Just drop them in copious boiling, salted water, allow the water come back to a boil (over high heat, it shouldn't take more than 30 seconds or so, covering the pan will quicken the return to a boil), then allow them to boil until they are the brightest possible green (that can take anywhere from a few seconds to a minute). Drain them like pasta and then plunge them in ice water to stop the cooking. Drain the ice water after the beans are cold.

You can do this part hours in advance if you like, that would make the final fry at meal time go super quick and easy. They will be evenly and perfectly done by just thoroughly heating through when you fry.

First off, 30 minutes seems like quite a long time, and stirring ten times seems like it should get things reasonably even. Perhaps you just like your beans really thoroughly cooked, but it does make me wonder if you might be using too small a pan, which would also make it difficult to stir thoroughly and contribute to uneven cooking. So make sure your pan is big enough that the beans on top of the pan are at least keeping warm. And if you aren't already, make sure that when you stir you're really getting the ones from the top down onto the bottom so everything can cook. I've certainly sauteed beans like this, and gotten fairly even cooking without stirring constantly.

That said, you can also save a lot of work by changing your cooking method. Jolene suggested blanching (a quick cook in boiling water, followed by rapid cooling), which will certainly work, but is also probably overkill if you just want to cook them right away. You can essentially steam them in your pan before sauteeing. Simply boil a bit of water in the bottom of your pan, toss in the beans, then either cover or stir constantly. They'll be cooked most of the way in a few minutes, then you can drain the excess water and proceed with sauteeing (no need to cool them). If you get the hang of it, all the water will have boiled off by the time you're ready to move on, and you won't even have to drain them. (And if it boils off too soon, it's easy enough to add a bit more.)

You could also consider simply roasting them. It's not quite the same, but it'll get you even better browning than sauteeing. Just toss the beans with a bit of oil, salt, and whatever seasonings you want, spread them out on a pan, and throw them in the oven for around 15 minutes at 425F. You might want to stir once halfway through, but if they're not piled up much, you can even get away with skipping that.

This is because you are not sauteeing them at all. You are baking them, and using the wrong heat source for a bake: the stove.

To saute beans, or other vegetables:

1. Start with room temperature vegetables, frozen won't work
2. Cut them up in small pieces. Larger vegetables need to be cubed, beans can be snapped in 3-4 cm long pieces.
3. Use a very hot pan
4. Put in just enough vegetables to cover the pan in a single layer
5. Keep the vegetables in movement, constantly. Usually done by shaking the pan, but you can also stir.

In about a minute, your batch is ready.

You can use the above method, which is proper sauteeing, but I don't know if this is what you want. It is less work to prepare them by another method. If what you want is to pour beans, oil and soy sauce into a vessel, put it on the heat and go do other things, do it in the oven. It will take more than 30 minutes, but you don't even have to stay in the kitchen during this time, and your beans will be evenly cooked through without any stirring. The actual cooking time will depend on your oven temperature, pan material, bean heap thickness and starting temperature (frozen or room temperature), so you'll have to experiment.

Other alternatives include simmering them in water, blanching them, steaming them, or cooking them in the microwave. I don't see much point in frying green beans.