Char the tomatillos and jalapeno either directly over a stovetop flame or under a broiler in the oven until they are blackened all over. This will take 3-5 minutes of constant turning over a flame and probably around 6 minutes of regular turning under a broiler. Place in a bowl, cover with plastic wrap, and let steam.

Peel off the blackened skin with a dampened paper towel and place the vegetables into a blender. Add in the onion, avocado, cilantro, a pinch of salt, and lime juice. Blend everything until the mixture is completely smooth. Taste the sauce and blend in more salt if needed. Transfer the sauce to an airtight container and refrigerate for up to 3–4 days.

Combine the masa harina, salt, and water in a bowl and mix by hand until it forms a shaggy dough. Knead together until it forms a smooth ball. Pinch off 40-50g pieces and place into a tortilla press lined with greased plastic wrap. Press until about ¼” (.6cm) thick and immediately place onto a preheated griddle set over medium heat. Cook for about 45 seconds then flip and cook for an additional 15-30 seconds. Remove cooked tortillas to a linen-lined plate, cover with another linen, and repeat with the remaining dough.

Preheat a flat griddle set over two burners, set one burner to medium heat and the other to medium-high (or use two cast iron pans). Once the griddle is hot, sprinkle a generous handful of grated quesillo (or Oaxaca) cheese directly onto the medium heat side, forming a rough circle about the size of a tortilla. As soon as the cheese begins to melt and bubble, place one tortilla on top of the melting cheese.

While the tortilla is setting into the cheese, place one slice of thinly sliced beef in a single layer on the medium-high side (next to the tortilla). Season to taste with salt and black pepper. Let the beef cook undisturbed for about 1 minute so it develops a good sear and browns nicely. Flip, season to taste again, and cook for about 30 more seconds, or until browned. Set aside the cooked beef until ready to assemble.

When the cheese under the tortilla has turned golden brown and formed a crisp layer (a cheese skirt), carefully flip the tortilla over so the cheese side is now facing up. Place the beef slice onto the cheese-covered side of the tortilla to assemble the taco. Move the finished taco off the pan and set it aside. Repeat the cheese melting, tortilla placement, and beef searing process for each remaining tortilla and batch of beef.

Top each taco with a spoonful of green salsa, a sprinkle of finely chopped onion, and cilantro leaves. Squeeze the lime wedges over the tacos once you’re ready to eat. Serve and enjoy.