Adjust an oven rack to the upper third of the oven and heat the broiler on high. Lightly oil a 9-by-13-inch baking dish (23-by-33-cm).
Place the poblano peppers on a rimmed baking sheet. Broil, turning every 2 to 3 minutes with tongs, until the skins are blistered and charred in spots on all sides, 10 to 12 minutes total.
Transfer the hot peppers to a bowl and cover tightly with a plate or plastic wrap. Let steam for 10 minutes. When cool enough to handle, gently rub away the loose skin. Leave the stem attached.
Make one lengthwise slit in each pepper, stopping short of the stem and tip. Carefully remove the seeds and membranes. Take care not to tear the peppers; a few remaining seeds are fine.
In a medium bowl, combine the Oaxaca cheese, Monterey Jack, salt, and cumin. Divide the cheese mixture among the peppers, gently pressing the slit mostly closed after filling.
Pour 1/2 cup (120 ml) of the enchilada sauce into the prepared baking dish. Arrange the filled peppers seam-side up in the dish and spoon the remaining 1/2 cup (120 ml) sauce around, rather than directly over, the peppers.
Bake at 375°F (190°C) until the cheese is fully melted and the sauce is bubbling around the edges, 15 minutes. Rest for 5 minutes before serving. Top with cilantro and queso fresco, if using, and serve with lime wedges.