For the tortillas: Combine the masa, water, shortening and salt in a bowl. Bring the mixture together with your hands and make into a uniform disc. Wrap the disk in plastic wrap and let rest at room temperature for about 20 minutes.
Preheat a large cast-iron pan over high heat. Line the tortilla press with parchment paper.
Portion the dough into golf-ball-size balls, about 1 1/2 ounces each. Place 1 ball at a time into the tortilla press between two sheets of parchment paper. Press down on the tortilla press. Carefully, peel away one sheet of the parchment. Flip the exposed side of the tortillas onto your hand and carefully remove the other side of the parchment. Place the tortilla directly onto the preheated skillet. Cook until the edges begin to curl and bumps form, 1 to 2 minutes. Flip and cook the other side, 1 to 2 minutes. Repeat with the remaining tortillas.
For the enchiladas: Combine the chicken, chicken broth, salt, garlic and onions in a large saucepan over high heat. Bring to a boil, and then reduce the heat, cover with a lid and simmer until the chicken is fully cooked, about 20 minutes. Remove the chicken and set aside to cool. When cool enough to handle, shred the chicken and set aside.
For the colorado sauce: Heat a medium skillet over medium-high heat. Toast the chiles skin-side up until fragrant and beginning to darken, 30 seconds to 1 minute. Transfer the chiles to a bowl and pour over the boiling water, or enough to cover the chilies; soak until softened, about 15 minutes.
Transfer the chiles and steeping liquid to the bowl of a food processor. Pulse until a smooth paste forms.
Heat the vegetable oil in a saucepan over medium heat. Add the coriander, cumin, garlic and onions and cook until softened and fragrant, 6 to 8 minutes. Whisk in the blended chile paste and bring to a simmer. Cook until slightly reduced and flavors are developed, 4 to 6 minutes. Sprinkle with salt and black pepper. Set aside.
For assembly: Pour 1/4 inch vegetable oil into a large frying pan over medium-high heat. Soften the tortillas one at a time in the hot oil, about 5 seconds. Set each tortilla on a paper towel afterwards to soak up some of the oil.
To assemble the enchiladas, dip a softened tortilla in simmering Colorado sauce and place on a work surface. Add 2 tablespoons shredded chicken and 1 tablespoon Colorado sauce. Roll up tightly and place on a serving platter.
Top the enchiladas with crumbled queso fresco, onions and cilantro. Drizzle with some crema, if using, and serve immediately.