Place the chicken in a pot, skin side down, then cover with water. Add the salt, pepper, and cumin then bring to a soft boil on medium heat. Once it begins to gently bubble, turn the heat down to low and simmer uncovered for 15 minutes or until the internal temperature is 150°F. (If using boneless, skinless parts, you’ll want to cook for about 8 minutes instead.)
Remove the chicken and place in a bowl. Strain the broth and return the broth to the pot.
When the chicken is cool enough to handle, remove the skin and bones then shred the meat with your hands. Toss with the lime juice.
Meanwhile, to make the 2 salsas—a salsa verde and a salsa rojo—place the tomatillos, tomatoes, garlic, jalapeño, and chiles de arbol in the pot with the broth. Bring back to a boil on high, then turn the heat down to low and simmer for 8-10 minutes or until softened. Turn off the heat.
With tongs or a slotted spoon, remove the tomatillos, garlic, and jalapeño from the pot and place in a blender along with 2 tablespoons of the broth from the pot. (Leave the tomatoes in the pot for now.) Add the cilantro to the blender then puree until smooth. Taste and add salt and cumin if desired. This is your salsa verde.
Pour the salsa verde out from the blender leaving in the blender 1/2 cup of the salsa. Add to the blender the tomatoes and chiles de arbol. Puree until smooth, then taste and add salt and cumin if desired. This is your salsa roja. You may keep the rest of the broth for another use.
To prepare the tortillas, pour enough oil in a heavy skillet to come up 1/2 inch up the sides and heat to 350°F, about 5 minutes. If you don’t have a thermometer, you can test the temperature by sticking a wooden spoon into the oil. If it bubbles around the spoon, it should be ready for frying. Line a large plate or sheet with paper towels.
Fry the tortillas on each side until softened and just beginning to brown, about 30 seconds. The key is to get them hot and pliable but not crisp and crunchy. Drain the tortillas on paper towels.
To prepare the chalupas, evenly spread on half of the tortillas the salsa verde, and evenly spread on the other half the salsa roja. Top each tortilla with the shredded chicken, queso fresco, diced onion, and cilantro. To eat, fold each in half as you would a taco and eat with your hands.
Notes
If you don't have chiles de arbol on hand, I'd add a few more grape tomatoes and another jalapeño instead for the salsa roja or 1 chipotle chile in adobo sauce. Likewise, the salsas and chicken can be made ahead of time. I use grape tomatoes as they're always fresh and flavorful, but if it's tomato season, you can substitute 2 ripe plum tomatoes instead.