Add all the chicken to a large pot. Add onion, garlic cloves, salt, and pepper. Add water. About 5-6 cups. Put a lid on the pot and cook for 30 minutes, or until the chicken is cooked through.
Remove the chicken from the pot and let cool slightly. Reserve all the liquid.
When the chicken is cool enough to handle, shred. Return the shredded chicken to the pot.
Add the hominy and oregano.
Pour remaining water into the pot. Add vegetable broth. Cover and bring to a boil.
Reduce heat and cook for 45 minutes. Serve and add desired toppings.
Making the Tortillas
In a large mixing bowl, combine the masa harina and salt. Gradually add water and stir the mixture with a spoon until an evenly mixed dough begins to form. Use your hands to knead the dough for 2-3 minutes in the mixing bowl until it is smooth and forms a cohesive ball.
Portion the dough. Use a spoon or a medium portion scoop to portion the dough into a 2-tablespoon ball, approx. the size of a golf ball. Then use your hands to roll the ball until it is nice and round.
Press the dough balls. Place the dough ball between two pieces of plastic in a tortilla press. Then gently press the dough ball until it forms a 4- to 5-inch tortilla.
Heat a non-stick skillet over medium-high heat. Once the pan is nice and hot, gently peel the tortilla away from the plastic wrap and lay the tortilla flat in the skillet. Cook the tortilla for about 40-60 seconds per side, flipping it once speckled brown spots begin to appear on the bottom of the tortilla.
Once it is cooked, transfer the tortilla to a tortilla warmer or a bowl wrapped in a clean kitchen towel, so that the tortillas do not dry out. Repeat with the remaining tortillas.
MASTERS CLASS ONLY
Heat vegetable oil in a large skillet over medium-high heat until shimmering.
Add corn, season with salt to taste and toss, then let cook, tossing only occasionally (about every 2 minutes) until corn is well charred all over (about 6 – 9 minutes total). Remove from heat and allow it to cool slightly.
Add corn to a bowl along with avocados, onions, cilantro, jalapeno, garlic, Cotija, mayonnaise, lime juice and chili powder and toss.
Serve immediately with more chili powder to taste as desired.