2 cups flour
3/4 cup salt (I like to use Kosher salt)
2 tbsps cream of tartar
1 Tbsp vegetable oil
2 cups water
Food coloring (optional)
Mix all ingredients. Put on medium heat, stirring constantly. Mixture will achieve the consistency of super-wet mashed potatoes. Keep stirring until dough comes away from the sides of the pot as you stir. It will start to grow a "skin," which lets you know it's almost done.
I take it off the heat as it gets less moist. I don't stop stirring, because it can burn easily, especially on an electric burner, where it's more difficult to adjust the heat.
Remove from pot and place on wax paper, wooden board, whatever you like. Allow to cool a minute or two, until you are able to handle it comfortably. You may need to add a couple fingerfuls of flour to the dough if it is too wet to handle. Knead the dough into a lovely, elastic, play-doughy goodness. I allow it to cool even more before I place it in an airtight container or ziplock bag.
It lasts for a while, though I'm not sure exactly how long, because I always give it away. One mom told me she kept it in the fridge for 3 months. I'm not sure if that would dry it out, so experiment. It can get moldy after a few weeks unrefrigerated -- I've had that happen.
It's definitely moister than store-bought play-dough, and it stretches into super long "snakes." It's also a fun project to do with pre-schoolers. I don't let such small kids use the stove top, but they can mix the ingredients with you ahead, you can stir, and they can help knead the dough once it's safely cool.
Another fun thing to do is to wait to add the food coloring until you knead the dough. The colors swirl and blend in fun ways, and kids dig it.
I have another recipe which uses alum -- it's a pickling preservative. I've lost it, but will look for it.
Go make some play-dough!