Place poblano peppers directly over gas burner flames or under the broiler, turning frequently until skin blackens and blisters completely, about 8-10 minutes. Transfer to a bowl, cover tightly with plastic wrap, and let steam for 10 minutes.

Peel away the blackened skin with your fingers or a knife. Remove stems and seeds, then slice into strips about ¼-inch wide.

Toss chicken strips with cumin, smoked paprika, oregano, salt, and pepper in a large bowl. Heat olive oil in a large skillet over medium-high heat until shimmering. Add chicken in a single layer, letting it sear undisturbed for 3-4 minutes until golden.

Add sliced onions to the pan with chicken, cooking for 3-4 minutes until they begin softening and developing golden edges. Stir in minced garlic and cook for another minute until fragrant. Add the prepared poblano strips, tossing everything together for 2-3 minutes until heated through.

Warm tortillas in a dry skillet for 30 seconds per side or wrap in damp paper towels and microwave for 45 seconds. Fill each tortilla with the poblano chicken mixture, then top with crema, crumbled queso fresco, and fresh cilantro. Serve immediately with lime wedges.