Step 1

Adjust oven rack to center position and preheat oven to 300°F (see note for pressure cooker instructions). Heat butter in a large Dutch oven over medium heat until melted. Continue to cook, swirling pan gently until butter is nutty-smelling and solids are a toasty brown. Transfer to a heatproof cup or bowl and reserve for Brown Butter Cornbread Crust.

Step 2

Return pan to high heat. Season skirt steak generously with salt and pepper. Add to the pan in as close to a single layer as possible. Cook without moving until deeply browned on bottom side, about 6 minutes. When beef is browned (do not brown top side), transfer to a large plate and set aside.

Step 3

Meanwhile, place chilies on a microwave-safe plate and microwave until hot, pliable, and toasted, about 30 seconds. Transfer to a microwave-safe liquid measuring cup and add 1 cup chicken stock. Cover with plastic wrap and microwave on high power until gently simmering, about 3 minutes. Remove from microwave and transfer to a blender. Add remaining chicken stock. Blend until completely smooth, about 1 minute. Set aside.

Step 4

Return Dutch oven to high heat. Add oil to Dutch oven followed by corn. Cook, stirring occasionally, until corn is well charred in spots, about 4 minutes. Add onion, bell pepper, and poblano pepper, and cook, stirring, until softened but not browned, about 3 minutes.

Step 5

Add garlic, Serrano pepper, cumin, coriander, and oregano and cook, stirring, until fragrant, about 30 seconds. Add chili purée and stir to combine. Return beef to the pot along with any drippings. Add olives and stir to combine.

Step 6

Bring to a simmer on the stovetop, cover, and transfer to the oven (see note for pressure cooker instructions). Cook until beef is fall-apart tender, about 2 1/2 hours. Remove from oven.

Step 7

Set oven temperature to 425°F. Stir Worcestershire sauce, fish sauce, and cheese into stew. Return to stovetop and simmer on medium heat, stirring frequently, until thickened to a rich, stew-like consistency, about 5 minutes. Stir in scallions and cilantro and season to taste with salt and pepper. Transfer mixture to a 12-inch cast iron skillet or a 9- by 13-inch casserole dish.

Step 8

For the Brown Butter Cornbread Crust: Combine cornmeal, flour, sugar, 1 teaspoon kosher salt, baking powder, and baking soda in a large bowl. Combine eggs, sour cream, and buttermilk in a second bowl and whisk until homogenous. Whisking constantly, slowly drizzle in reserved browned butter. Whisk wet ingredients into dry ingredients until homogenous.

Step 9

Using a large spoon, place small dollops of the cornbread batter mixture on top of the beef filling, then use the back of the spoon to spread it into an even layer. Transfer the skillet to the oven and bake until pale golden brown and a skewer inserted into the cornbread comes out clean, about 20 minutes.

Step 10

Let cool 15 minutes, then serve with sour cream.