Combine the cabbage, carrot, onion, vinegar, water, oregano, sugar, salt, and pepper in a large bowl. 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 medium bowl. Season with salt and pepper to taste.

Stir the masa, water, and salt together with a rubber spatula in a large bowl until a soft dough forms. Knead the dough in the bowl for about 1 minute until it is soft and slightly tacky but no longer sticks to your hands. Cover the dough with a damp paper towel to prevent it from drying out.

Cut apart the sides of a small zipper-lock bag, leaving the bottom seam intact to create a plastic folder. Pinch off a portion of dough and roll it into a ball, keeping the remaining dough covered. Using slightly wet hands, flatten the dough into a 4-inch round and place a portion of the cheese mixture in the center. Bring the sides of the dough up to enclose the filling and pinch the top to seal. Press the ball into a 1-inch-thick disk, place it inside the plastic folder, and use a large plate to gently press it into a 1/4-inch-thick pupusa. Repeat with the remaining dough and filling.

Heat the oil in a 12-inch nonstick skillet over medium-high heat until shimmering. Wipe out the skillet with a paper towel to leave only a thin film of oil. Cook the pupusas in batches for about 3 minutes per side until they are spotty brown and the dough is cooked through. Transfer to a platter and serve warm with the slaw.