Toss the cabbage, carrot, vinegar, water, cilantro, jalapeño, sugar, and oregano in a large bowl. Season with salt and pepper to taste and let the mixture sit for at least 30 minutes; the cabbage should soften slightly and the flavors will meld as it rests.

Combine the Monterey Jack, scallions, cilantro, lime juice, and chili powder in a medium bowl. Season with salt and pepper to taste and mash with a fork until the mixture is uniform and slightly tacky.

Mix the masa harina, warm water, vegetable oil, and salt in a large bowl until a smooth, pliable dough forms. Let the dough rest for about 5 minutes; it should feel like damp sand and hold its shape when squeezed without cracking.

Divide the dough into 10 equal portions and roll them into balls. Using your thumb, create a deep indentation in each ball to form a small cup, then place a portion of the cheese filling into the center.

Pinch the edges of the dough over the filling to seal it completely, then gently press the ball between your palms to flatten it into a disk about 4 inches wide and 1/2 inch thick.

Heat a large cast-iron skillet over medium-high heat until a drop of water flicked onto the surface sizzles and evaporates immediately. Lightly coat the pan with oil and cook the pupusas in batches until they are golden brown and spotted on both sides, about 3 to 5 minutes per side.

Serve immediately while the cheese is molten and the edges are crisp, topped with a generous mound of the chilled cabbage slaw.