Poaching the chicken. If the chicken breast halves still have their wings attached, cut the final two joints off the wings (this makes for a nicer-looking presentation). Into a large (6- to 8-quart) pot, measure 10 cups of water. Add half of the onion, half of the garlic, the marjoram, thyme, bay and 1 ½ teaspoons salt. Bring to a boil, then add the chicken breasts and simmer, uncovered, over medium heat for 10 minutes. Cover the pot and let stand off the heat for 10 minutes. Remove the chicken from the pot. Strain the broth and skim off any fat that rises to the top.
The sauce. In a heavy medium-size (4-quart) pot, Dutch oven or Mexican cazuela, dry-toast the pumpkin seeds: Set the pot over medium heat, add the pumpkin seeds and, when the first one pops, stir constantly until all have popped from flat to round, about 5 minutes. Don’t let them darken past golden (usually caused by too high a heat or not enough stirring) or the sauce will be brownish and slightly bitter. Cool the pumpkin seeds, set aside 3 tablespoons for garnish and transfer the rest to a blender.
Add the remaining half of the onion and garlic to the blender along with the tomatillos, lettuce, chiles, epazote and cilantro. Pour in 1 cup of the strained broth and blend to a smooth puree.
In the pumpkin seed-toasting pot, heat the oil over medium-high. When hot enough to make a drop of the puree sizzle sharply, add it all at once. Stir as the mixture darkens slightly and thickens considerably, about 10 minutes. Stir in 2 cups more of the broth, reduce the heat to medium-low and simmer about 20 minutes for the flavors to mellow and the sauce to thicken to a medium consistency (it should coat a spoon nicely).
Finishing the dish. While the sauce is simmering, steam the chayote in a vegetable steamer for 3 minutes. Then add the zucchini and steam 2 to 3 minutes more, stirring everything several times to ensure even cooking. (If you find it easier you can blanch the vegetables in salted boiling water—cook the chayote for 3 minutes, then add the zucchini for a final minute of boiling). Drain and spread out the vegetables on a plate to stop the cooking.
When the sauce has simmered 20 minutes it will likely look coarse; I prefer to smooth it to a velvety texture by re-blending it in small batches (loosely covered to avoid blender explosions). Return the sauce to the pan, taste it and season with salt, usually about ¾ teaspoon. If the sauce has thickened beyond a light cream-sauce consistency, thin it with a little of the remaining broth. Slip the cooked chicken breasts into the sauce, then add the cooked vegetables. Simmer over medium heat just long enough to heat everything through (about 5 minutes), then spoon chicken, vegetables and sauce out onto a warm serving platter. Sprinkle with the reserved pumpkin seeds (you may want to roughly crush them), decorate with epazote or cilantro sprigs, and you’re ready to offer a unique experience to your guests.
Working Ahead: The chicken may be poached and the sauce made a day ahead; store them separately, covered, in the refrigerator. Let the chicken warm to room temperature before heating it in the sauce. The vegetables are best cooked shortly before you serve them.