Salsa Verde:
1 Tbsp. vegetable oil
1/2 white onion, coarsely chopped
4 garlic cloves, crushed
3 small serrano chiles, halved lengthwise, seeds removed if desired
12 oz. tomatillos (6–7), husks removed, rinsed, halved
1 cup cilantro leaves with tender stems
Kosher salt
Salsa Roja:
1 Tbsp. vegetable oil
1/4 white onion, coarsely chopped
1 garlic clove, crushed
3 guajillo chiles, seeds removed
2 dried chiles de árbol (optional; omit for a milder sauce)
3 plum tomatoes, quartered
Kosher salt
Enchilada assembly:
1 (3 1/2–4-lb.) chicken
6 bay leaves
1 tsp. allspice berries
Kosher salt
1/2 cup crème fraîche
1/3 cup crumbled queso fresco
1/2 cup vegetable oil
12 (6") corn tortillas
Sliced white onion (for serving)
Salsa Verde:
Heat oil in a large saucepan over medium. Cook onion and garlic, stirring occasionally, until starting to soften, about 5 minutes. Add chiles and cook, stirring occasionally, until onion is lightly browned and vegetables are soft, about 5 minutes. Add tomatillos and cook, stirring occasionally, just until starting to soften, about 3 minutes. Add cilantro and 1 1/2 cups water. Bring to a boil, reduce heat, and simmer until tomatillos soften, 20–25 minutes. Let cool slightly; transfer to a blender. Purée until smooth; season with salt. Return salsa verde to saucepan and keep warm until ready to use.
Salsa Roja:
Heat oil in a large saucepan over medium. Cook onion and garlic, stirring occasionally, until starting to soften, about 5 minutes. Add both chiles, tomatoes, and 1 1/2 cups water. Bring to a boil, reduce heat, and simmer until tomatoes and chiles soften, 20–25 minutes. Let cool slightly; transfer to a blender. Purée until smooth; season with salt. Return salsa roja to saucepan and keep warm until ready to use.
Enchilada assembly:
Place chicken, bay leaves, and allspice in a small pot and pour in water to cover by 1"; season lightly with salt. Bring to a boil, reduce heat, and simmer gently until chicken is nearly cooked through (an instant-read thermometer inserted into the thickest part of chicken should register 145°F–150°F), 20–25 minutes from the time water starts simmering. Let chicken cool at least 1 hour (it should be just warm). If you have the time, cover and chill up to 12 hours.
Remove chicken from broth. Pull meat from bones and shred; discard skin and bones. Place meat in a large saucepan and pour in just enough broth to cover. Set aside any remaining broth for another use. Gently reheat chicken over medium-low; season with salt.
Meanwhile, mix crème fraîche and queso fresco in a small bowl to combine.
Heat oil in a small skillet over medium-high until hot but not smoking. Submerge each tortilla in oil long enough to soften but not so long that they fall apart, 5–10 seconds each. Transfer to a rimmed baking sheet lined with paper towels to drain.
Working one at a time, fill each tortilla with about 1/3 cup shredded chicken and roll up tightly. Place 3 tortillas each, seam side down, into bowls. Ladle 1/2 cup of each sauce on opposite ends of enchiladas. Top with a big spoonful of crème fraîche mixture and scatter onion over.