Bring 10 cups water to a boil in a large saucepan over medium heat. Add tomatillos and chiles. Boil tomatillos for 8 minutes or until they darken in color. Transfer to a blender. Continue boiling chiles for 5 minutes more or until they darken in color. Remove from heat, cut off stems and add to blender. Add onion, garlic, cilantro, and salt. Blend until smooth.

Heat oil in a large skillet over medium heat. Add blended sauce. Simmer for 10 minutes, stirring frequently. Transfer to a bowl and set aside. 

Combine masa harina and warm water in a large bowl. Knead until masa is smooth and not sticky. Form into a large ball and cover in bowl with a clean kitchen towel. Let rest for 15 minutes. Measure out 22 masa balls (25g in weight). 

Preheat a comal or griddle over medium heat. 

Using a tortilla press with plates lined with two plastic sheets, press masa balls into small tortillas. Heat each tortilla on comal for 60-90 seconds on each side or until the edges begin to toast. Transfer to a kitchen towel or tortilla warmer. Repeat until all tortillas have been cooked. 

Heat oil in a large skillet. Working quickly and carefully, place tortilla in hot oil; Do not flip. Add 2 tablespoons of salsa verde on tortilla, 3-4 strips of Oaxaca Cheese and 2 tablespoons cactus while bottom side I of the tortilla is frying; 30-60 seconds. Remove from oil and place on a serving plate. Repeat with remaining tortillas.

Top chalupitas with queso fresco, onion and tomato. Serve.