In a large mixing bowl, combine masa harina and broth. Stir until thoroughly incorporated.

Combine lard, salt, and baking powder and, using an electric mixer, beat at medium-high speed until lightly whipped, about 1 minute.

Add ¼ of the re-hydrated masa at a time to the lard, beating between additions until thoroughly incorporated. The masa should be soft and spreadable, with a hummus-like texture.

Cover masa with plastic and refrigerate for 1 hour.

Meanwhile, for the filling: Microwave ancho chiles until fragrant and pliable, 15 to 30 seconds. Transfer to a microwave-safe bowl or measuring cup, add broth, cover tightly with plastic wrap, and microwave on high power until barely simmering, about 3 minutes. Let steep for at least 5 minutes. Using a blender or immersion blender, blend until smooth.

In a skillet, heat lard over medium-high heat until shimmering. Add onion and garlic and cook until softened, about 3 minutes. Add beans and cook until heated through. Using a potato masher, bean masher, or wooden spoon, mash beans to form a chunky purée. Stir in ancho mixture and cook, stirring, until thickened, about 5 minutes.

Preheat oven to 375°F (190°C). Remove masa from refrigerator, discard plastic, and re-whip, adding water one tablespoon at a time, if necessary, to return it to original hummus-like texture.

Lightly grease a 12-inch cast iron skillet or 3-quart casserole dish with cooking spray or oil, wiping up any excess.

Scrape ⅔ of masa into skillet and press to form an even thin layer on bottom and edge of pan.

Add 2 cups of black bean filling, smoothing to an even layer. Save any remaining filling for another use.

Gently form a top crust with remaining ⅓ masa, binding it with edge.

Wipe any masa residue from rim of skillet. Bake tamale pie until cooked through and lightly golden on top, 45 minutes to 1 hour. Let cool slightly, then slice and serve, passing hot sauce and salsa verde at the table.