When making this dish, I have found that it is best to use fresh spices or dried spices. Seasoning spices mixed with salt does not particularly go well with all the other ingredients added.
Make the béchamel sauce: heat butter in a saucepan and add flour. Stir to blend (best to use a wooden spoon). Once butter and flour are well mixed, gradually add milk while stirring. When milk is fully incorporated, add grated cheese. Stir and let mixture cook for about 2 to 3 minutes on low heat. Mixture should be thick. Remove from heat and set aside. In a large bowl, mix chayote with meat mixture; fold in béchamel sauce.
The chayotes will release more water as they cook, so the béchamel sauce must be thick. Drain them thoroughly before mixing all ingredients.