Combine the cabbage, carrot, onion, vinegar, water, and oregano in a bowl and season with salt and pepper. Cover and refrigerate for about 1 hour to allow the cabbage to wilt slightly and the flavors to develop.

Mix the Monterey Jack, scallions, cilantro, lime juice, and chili powder in a separate bowl and season with salt and pepper to taste.

Stir the masa harina, water, and salt together with a rubber spatula until a soft dough forms. Knead the dough by hand for about 1 minute until it is soft and slightly tacky; it should feel like playdough and no longer stick to your fingers. Keep the dough covered with a damp paper towel to prevent it from drying out.

Prepare a small zipper-lock bag by cutting open the sides while leaving the bottom seam intact. Using wet hands, flatten a portion of dough into a round, place the cheese filling in the center, and pinch the edges together to seal the filling inside. Place the dough ball inside the plastic bag and press gently with a large plate until it is a thin, even disk.

Heat the oil in a nonstick skillet over medium-high heat until it shimmers, then wipe most of it out with a paper towel to leave just a thin film. Cook the pupusas in batches for about 3 minutes per side until they are spotty brown and the cheese inside is melted.

Serve warm with the chilled cabbage slaw on the side.