Bring 2 cups water, chicken, garlic, bay leaves, salt, and peppercorns to simmer in medium saucepan over high heat. Reduce heat to maintain simmer and cook until chicken registers 160 degrees, 5 to 7 minutes. Transfer chicken to bowl and let sit until cool enough to handle, about 5 minutes (strain broth and reserve for other use). Shred chicken into ½-inch pieces.
For the green sauce:
Place tomatillo salsa in blender. Add cilantro, sugar, and salt and blend until smooth, about 1 minute. Add crema and blend until smooth, 45 to 60 seconds.
For one pan enchiladas
Line rimmed baking sheet with double layer of paper towels. Heat oil in 10-inch oven safe skillet over medium heat to 325 degrees. Using tongs, place 1 tortilla in skillet and fry for 5 seconds. Flip tortilla and continue to cook until it is puffed in spots but not browned, 4 to 6 seconds longer. Transfer to prepared sheet. Repeat with remaining tortillas. Place double layer of paper towels over tortillas and press to absorb excess oil. Discard oil and wipe out skillet.
Adjust oven rack to middle position and heat oven to 425 degrees. Add oregano to chicken and toss to combine. Season with pepper to taste. Spread ¼ cup sauce across bottom of now-empty skillet.
Place ¼ cup chicken over lower third of 1 tortilla. Sprinkle about 2 Tablespoons Monterey Jack cheese over the chicken. Roll tortilla tightly around filling and place seam side down in skillet. Repeat with remaining tortillas and filling. (Arrange 6 enchiladas down center of skillet and one on each side). Spread ⅓ cup sauce evenly over enchiladas. Sprinkle remaining Monterey Jack evenly over sauce. Bake until cheese is melted and filling is heated through (internal temperature should be between 135 and 140 degrees), about 12 minutes.
While enchiladas bake, transfer remaining sauce to saucepan and bring to gentle simmer over medium-high heat, stirring occasionally, about 5 minutes. Divide sauce evenly among 2 shallow bowls. Arrange 3 enchiladas in each bowl, over sauce. Garnish enchiladas with cilantro, radish, cotija, and chopped onion. Serve immediately.
Video
Notes
TO MAKE AHEAD: Chicken can be refrigerated for up to 2 days. Sauce can be refrigerated for up to 24 hours. Tortillas can be kept covered at room temperature for up to 3 hours. Assembled enchiladas and remaining sauce can be refrigerated for up to 24 hours. Bake enchiladas in 400-degree oven until heated through, 15 to 18 minutes.