Char the poblanos under a broiler or over a gas flame, turning until blistered on all sides, about 8–12 minutes. Transfer to a covered bowl and let steam 10 minutes.

Rub off the loosened skins. Remove stems and seeds, then cut the peppers into strips.

Melt the butter in a skillet over medium heat. Cook the onion for 5–7 minutes until soft. Stir in the garlic for 30 seconds.

Add the poblano strips, salt and pepper and cook for 2 minutes. Reduce the heat to low, stir in the crema and warm gently for 3–4 minutes without boiling.

Add the Oaxaca cheese and stir until melted. Remove from heat, add lime juice, and sprinkle with cilantro if desired. Serve warm with tortillas.