Cover corn husks with very warm water in a large bowl. Weight them with a plate and soak for at least 30 minutes, until flexible. Prepare the filling and masa during this time. Keep extra husks for lining the steamer and replacing torn wrappers.

Place tomatillos, jalapeño, onion, and garlic in a saucepan and add water just to cover. Simmer for 10–12 minutes until tender. Drain, reserving a little cooking liquid. Cool briefly. Blend vegetables, cilantro, and salsa salt until smooth, adding a splash of reserved liquid only if necessary. When blending warm ingredients, vent the lid and cover it with a towel.

Heat oil in the empty saucepan over medium heat. Add salsa and simmer for 8–10 minutes until slightly thickened, stirring. Fold in cooked shredded chicken and simmer for 2 minutes. Transfer to a bowl to cool. Filling should be moist but not runny; reserve any excess loose sauce for the table.

Whisk masa harina, baking powder, and masa salt. Beat soft lard or shortening in a large bowl with a mixer for 3–4 minutes until lighter. Beat in masa mixture and 3 ½ cups warm broth in alternating additions. Continue beating for 4–5 minutes. The masa should spread like soft hummus; add additional broth 1 tablespoon at a time if stiff. Let stand for 10 minutes, then recheck the consistency.

Drain and pat husks dry. Choose 24 wide intact husks. With the broad end nearest you, spread about ¼ cup masa in a rectangle on the broad lower portion, leaving side margins and the tapered upper third bare. Put 3 tablespoons chicken filling down the center. Fold the long sides inward so masa encloses the filling, then fold the tapered empty end up. Leave the broad end open. Repeat; divide any remaining masa among the tamales without overfilling.

Add water below the steamer rack without letting it touch the tamales. Line the rack with spare husks. Stand tamales with open ends upward, supported loosely by a heatproof ramekin if needed. Do not pack tightly. Cover with spare husks and the pot lid. Bring to a steady simmer.

Steam for 75–90 minutes. Check water periodically and add hot water down the side of the pot, away from the open tamales. Do not let the pot boil dry. To check, remove one tamal with tongs and let it stand for 5 minutes. The husk should peel away cleanly and the masa should be set, not wet paste. If it sticks, steam another 10–15 minutes and check again.

Turn off the heat and let tamales rest in the covered steamer for 15 minutes so the masa firms. Remove carefully with tongs. Serve warm and remove the corn husks before eating.