Place an oven rack 4 - 6 inches from the broiler. Preheat broiler in oven (or heat grill).

Place poblano peppers under the broiler and roast for about 5 minutes, until skin is blistered and blackened all over. Flip peppers over and repeat.

When peppers are blackened all over, remove from heat and seal them in a plastic bag or put in a bowl and cover tightly with plastic wrap. Let them sweat for 5 - 10 minutes.

Transfer to a cutting board, then peel the thin, blackened skin from the peppers. Slice them open and remove the seeds, stem, and membranes, then slice into 1/2" strips. Set aside.

Heat oil over medium heat in a large skillet. Sauté onions until they just begin to take on color, about 10 -12 minutes. Lower heat to medium low, add garlic and stir to combine.

Add poblano strips, salt, pepper, Mexican crema, and oregano if using, to the onions. Stir to combine and let it warm through for 2 - 3 minutes.

Add Oaxaca cheese and stir frequently over low heat until cheese is completely melted.

Serve while warm.