The main ingredients are mangos, coconut milk and sugar, with a little bit of rice flour. Coconut milk is sold in 16oz cans and you can buy it either sweetened or unsweetened, low fat or regular. I used the unsweetened full fat variety it should work with any kind (just don't add extra sugar if you buy the sweetened variety).
You will also need calcium lactate and sodium alginate (to give your egg yolk the right shape and texture) and agar agar for the egg white. Sodium alginate and agar are extracted from seaweed, and calcium lactate, despite its name, is NOT made from milk (it is made by reacting lactic acid with calcium carbonate. Lactic acid, in turn is made with sugar, water and chalk). This desert is 100% vegan fun.
For tools you will need a hand blender and a small slotted spoon.
Although you might be able to find the ingredients locally and individually, it is much easier to buy a kit online. Molecule-R Cuisine R-Evolution Kit is fairly expensive but has very pretty packaging, and it's convenient because you'll get a good sample of ingredients and all the specialized tools too. It is from their DVD that I got the idea for this recipe: they give instructions for a reconstructed egg, but they didn't take the concept to its logical conclusion, they didn't make it vegan. Their egg white is made with regular milk, and doesn't taste as good as this version. You can also buy food grade sodium alginate , Calcium Lactate and Agar Agar Powder separately.