Rinse the dried shrimp and soak them in water for 30 minutes. Once soaked, drain the water.
Using a vegetable peeler, peel the skin off the chayote. If your chayote has ridges on the sides, you may need to use a paring knife to cut off the skin from the ridges.
Slice off the top of the chayote. Place the cut side down and slice the chayote in half. Slice off any skin that’s still stuck to the bottom ridges of the chayote. Dig out the seed with a knife or spoon.
Slice each half of the chayote lengthwise, so that you now have 4 sections. Slice each section into 1/4 to 1/2-inch slices. Give the chayote slices a quick rinse and drain them.
In a wok (or a sauté pan), heat the oil over medium-high heat. Add the shallots, garlic, ginger, and dried shrimp. Cook for 1 to 2 minutes. Then, add the chayote.
Add the water (or broth), salt, and chicken bouillon powder, if using. Stir everything together.
Cover the wok with a lid and continue cooking the chayote for 7 to 8 minutes, until the chayote is fork tender. I like to bite into a slice to make sure the texture is to my liking. I want them soft but still a bit firm (i.e., not completely mushy). Be careful if you do this as the chayote is very hot. Taste the broth and add more salt, if necessary.
Transfer the chayote to a serving bowl. Garnish with sliced scallions and sesame seeds.