I'm not sure where you get green mangoes in Cambridge, but summer is y-cumen in, so maybe someone will be selling them.
Since this recipe requires no measuring (just eyeballing), it works even in worlds where the meter stick is less than a meter long, the baker's cup holds a hogshead, and the scoville unit measures the amount of vanilla in a bean. Denizens of inverted spectrum worlds beware: eyeballing may not work properly there.
green mangoes, 5 or so (don't use ripe ones!)
mustard oil, several tablespoons
Julienne the mangoes and mix them with salt until they are coated. The ideal vessel for this activity is a pan with vertical sides, because you need to press the mangoes to get all the water out. I put a plate on top of them and something heavy (usually an economy-sized tub of vinegar) on top of the plate, then leave them overnight. Once the mangoes are pressed, rinse and drain them. Mix in fresh chilis, white vinegar, chili powder, and asafoetida to taste. Put the mango mixture in whatever container you plan to store it in. Heat the mustard oil over a medium-high stovetop, drop a handful of mustard seeds in, cook them until they pop, and take the mixture off the heat immediately. (I have found that pouring it out of the pan and into another vessel helps prevent burning, if you mess up the timing on the delicate mustard-seed-popping procedure.) Once the mustard oil has cooled, pour it over the mango mixture, seeds and all. If the oil has seeped into all the cracks between the mango bits and still covers the top of the mixture, great; otherwise, add more oil.
Leave the mixture to stew for about a week. (I've heard you can keep it at room temperature, but I always put it in the fridge.) Then share and enjoy.