There is hardly any good info about green papaya out there. Even a source that's usually reliable for me is contradictory - Purdue New Crop site. Most repeat that green papaya is poisonous or at least inedible raw! At first I thought that Katie was wrong and that any papaya picked green would work. That IS true with mangoes (I used to live where they grew - and maybe I should just say most mangoes). But since I am not near any papaya growing region I can't test this out. Regardless, I've never seen green-enough papayas in the regular supermarket. They are all ones that are ripe or semi-ripe, and unsuitable for Som Tum - Green Papaya Salad. I have to go nearly 100 miles to get these. There was a thai restaurant here but alas no more.
However, I like the salad with green mango (Som Tum Mamuang) even better. You might like it too? Just sub green mangos - with the peel. Find unripe mangoes that are as firm as possible as color is not a reliable indicator, some green ones can be quite ripe. This version is especially good with dried shrimp, not always put into the green papaya version (I like to heat them in oil till crispy first - I learned this from a restaurant I liked), but some people simply soak them or just add them dry. Some people can't stand these so be aware and perhaps leave these as an add-to-your-own plate accompaniment. I've made this with fresh shrimp too - boiled and chilled - grilled could work too. You need a bit less lime or tamarind (depending on the recipe) as the green mango is pretty sour. Now again, true hard, green mangoes are hardly ever found in the local grocery store, but for this salad, partially green ones work just fine, maybe even better.
Lastly, I experimented with zucchini - and it turned out great! I made a "Som Tum" with a mixture of Zucchini and green mango - shredded with a mandoline, and it's really tasty. I try to substitute local ingredients into SE Asian dishes that approximate ingredients that I can't get here - both for expediency, and to use my garden produce. Tomatilloes, for instance can sub for tamarind in some dishes where sour is desired (it of course can't sub for the raisin - molasses notes).
Here's my recipe:
4 cups julienned zucchini (from a larger firm one)
1 green mango julienned - as green (firm) as you can find. You could leave this out if you want, but I had one.
3 tomatoes chopped roughly
8 long beans broken into 3 inch lengths (asparagus, yard-long, snake beans) or sub green beans but you may have to blanch these if they are not great raw
1 lime juiced (or more depending on the size) - about 2-3 TBL
1 TBL tamarind water (make it from soaking tamarind pulp, or use concentrate) optional
4 cloves garlic chopped or more
2 hot green chiles (bird or cayenne) chopped - or more, red will work too as will chile paste if that's what you have
2 TBL fish sauce
1 TBL palm sugar (or brown or regular) broken up
3 TBL dried shrimp - crisped (shallow fried) in a little oil
3 TBL roasted peanuts chopped (I leave them halved whole if they are small)
Salt - you may need a bit - depending on the saltiness of the fish sauce and shrimp (these are sometimes salty)
Mix the veges. This is traditionally pounded together, so be a bit rough, especially with the beans and tomatoes to break them up a bit. Add the other ingredients and mix well. if you use palm sugar you may have to break it up or buzz it in a blender or water-proof grinder with the liquid ingredients or it won't mix properly (letting the salad sit for awhile can work too). The zucchini will exude more water than papaya but this is OK, you can pour it off if you like and replace some of the sauce ingredients. I found that the juice was fine left in - I strain some of the salad on a plate with some sticky rice - and pour on a little juice on the rice. You can always alter the taste of this to your own liking when serving with more lime, sugar, chile, or fish sauce. Lettuce or cabbage (Chinese usually), and herbs (basil, cilantro, etc.) can accompany this too.
If you do have a large mortar and pestle - start with the garlic, chiles, and palm sugar and grind well, add the peanuts and grind till chopped, then add the beans and tomatoes and roughen, then all the rest, pounding and mixing as desired. You may have to leave out the zucchini and just add this last to a bowl as it makes a lot and probably won't fit into the mortar.