For the Chicken:
1/4 cup olive or vegetable oil
Juice of 1 lime, about 3 tablespoons
3 to 4 cloves garlic, crushed
1 tablespoon fresh thyme, chopped
1 teaspoon ground cumin
1 teaspoon paprika or smoked sweet paprika
1 teaspoon honey or light agave
2 pounds boneless, skinless white- or dark-meat boneless, skinless chicken, pounded to 1/2-inch
Salt and pepper
1/2 cup chicken stock
For the Poblano Pepper and Tomatillo with Crema:
4 large poblano chili peppers, seeded and halved
1 large or 2 small tomatillos, peeled
1 tablespoon olive or vegetable oil
1 small onion, finely chopped
2 cloves garlic, finely chopped
1 scant teaspoon ground cumin
1/2 teaspoon dried Mexican oregano
3/4 cup Mexican crema, crème fraiche or heavy whipping cream
Salt and pepper
Juice of 1/2 lime
1/2 to 1 teaspoon honey or light agave
For Soft Tacos/Fajitas:
16 6-inch corn tortillas (for soft tacos) or flour tortillas (for fajitas)
1 1/2 cups each shredded Swiss (Emmentaler) and Monterey Jack or Chihuahua cheese
Chopped lettuce or white cabbage
Very thinly sliced radishes
Quick pickled red onions: very thinly sliced 1 red onion, combined with 1 thinly sliced jalapeño, juice of 1 lime, salt and pepper. Let stand 20 minutes.
Cilantro or parsley, coarsely chopped
For the chicken, whisk up marinade in shallow dish, add meat and season with salt and pepper. Turn chicken to coat and marinate half an hour.
Heat a large, cast-iron or heavy skillet over medium-high. Add chicken, cook 8-10 minutes, turning occasionally, under loose foil then remove to a cutting board. Add stock to pan to loosen drippings, slice chicken and return.
While chicken is still marinating, for peppers, heat broiler and leaving door ajar for steam to escape, char peppers and tomatillo until skins are blackened. Cool in covered bowl then peel most of skin from peppers and slice. Finely chop or puree tomatillos (about ½ cup), reserve.
Heat skillet over medium heat with 1 turn of the pan of oil, add onions and garlic, cumin, oregano, stir 2-3 minutes, add crema or crème or cream and reduce to thicken a minute or 2, stir in peppers, tomatillo puree, salt, pepper, lime juice, honey, reduce heat to low or cover pan to keep warm.
Char tortillas over open flame or in dry skillet over high heat to blister and loosen. Keep warm in tortilla warmer or wrapped in towel and foil in 175 oven. Prepare toppings while tortillas stay warm.
Serve slice chicken with poblanos in crema, fill tortillas and top with cheeses, lettuce, radishes, pickled onions and cilantro or parsley.