Step 1

Arrange racks in the upper and lower thirds of the oven and preheat to 450 degrees F.

Step 2

Place the chicken on a rimmed baking sheet and brush with 2 tablespoons of the oil. Roast on the lower rack until the skin is lightly golden and the chicken is cooked through, 40 to 45 minutes. Let sit until cool enough to handle.

Step 3

While the chicken is roasting, spread the tomatillos, garlic, jalapenos and onion on a second rimmed baking sheet. Roast on the top rack, tossing once or twice, until the tomatillos are tender and the jalapenos are browned and very tender, 30 to 40 minutes. Let cool.

Step 4

Once the chicken is cool, discard the skin and bones and shred the meat into 1/2-inch pieces. Put into a large bowl and set aside.

Step 5

Meanwhile, char the poblanos. Turn your gas burner to high. Place 2 to 3 poblanos directly on the grate and roast, turning with tongs every 3 to 4 minutes, until the entire pepper is blackened and very tender, 8 to 10 minutes. Transfer to a large heatproof bowl and repeat with the remaining poblanos. (Alternatively, if you have an electric stove, arrange the poblanos on a rimmed baking sheet and broil on high as close to the heat source as possible, turning occasionally, until the peppers are charred on all sides, 15 to 20 minutes. Transfer to a large heatproof bowl.)

Step 6

Wrap the bowl tightly with plastic wrap and let the poblanos steam for 15 minutes to loosen their skin. When they are cool enough to handle, peel all the blackened skin from the peppers; it's ok if there are flecks of black on the flesh or if some of the green skin is difficult to peel off. Split the sides open to remove the seeds, rinsing under cold running water if needed. Transfer the cleaned peppers to a blender.

Step 7

Remove the skin from the garlic cloves and add to the blender along with the tomatillos, jalapeno, onion and any accumulated juices. Add the coriander, cumin, oregano and a 1 ½ teaspoons of salt and puree on medium-low speed until smooth. Add the cilantro and puree on low speed until the cilantro is chopped but you can still see pieces of it in the sauce. Transfer the sauce to a large bowl and generously season with salt. You should have about 5 cups.

Step 8

Toss the reserved chicken with 3/4 cup of the salsa verde in a large bowl and generously season with salt.

Step 9

Heat the remaining 1 cup oil in a medium skillet over medium-high heat until it bubbles immediately when you touch the edge of a tortilla to the surface. Working with one at a time, fry the tortillas, turning once, until just starting to brown, about 10 seconds per side; the tortillas should still be pliable. Transfer the tortillas to paper towels to drain. Repeat with the remaining tortillas.

Step 10

Dip both sides of each tortilla in salsa verde to coat, and then transfer to a large plate. Spread 1 cup of the salsa verde evenly over the bottom of a 13-by-9-inch glass baking dish. Working with one tortilla at a time, spoon about 1/4 cup of the chicken filling across the center of a tortilla. Then fold one side of the tortilla over the filling and roll up the enchilada. Place them seam-side down in the prepared baking dish as you go (they should be nestled right up against each other). Top with any remaining salsa verde.

Step 11

Wrap the dish tightly with foil and bake on the upper rack until the sauce is bubbling and the tortillas are beginning to brown, 20 to 25 minutes. Let sit for 10 minutes.

Step 12

Meanwhile, whisk together the creme fraiche and milk in a small bowl. Season with salt.

Step 13

Top the enchiladas with the queso fresco, crema, cilantro leaves and onion slices. Serve with lime wedges for squeezing over.