In a large saucepan, bring 2 quarts of water to a boil over high heat. Add the salt. While the water is coming up to a boil, prepare a large bowl of ice water.

Cut the chayotes in half and remove the seed from the center. Add them to the pot one by one, reduce the heat to medium, and cook for 25 minutes, or until the chayotes are easily pierced with a knife.

Carefully remove the chayotes from the pan one half at a time, place them dry with a paper towel. 

While the chayotes are boiling, preheat the oven to 375 degree F. Spray rimmed baking sheet with cooking spray. 

Scoop a layer of flesh from each chayote’s—-about half, so the shell retains their shape—– and put the flesh in a large bowl. Arrange the chayote’s cut-side up on the prepared baking sheet.

Mash the reserved chayote flesh and fold picadillo and feta cheese until well combined and the mixture holds together well. Carefully scoop into the hollowed-out chayotes.

Place in the center rack of the oven and bake for 10 to 15 minutes until heated through and the top is browned. Remove from the oven and serve.