Slice the tops off the bell peppers and remove the seeds and membranes. Dice any usable flesh from the tops and set aside. If a pepper won't stand up, shave a thin sliver off the bottom without cutting through.
Heat a large skillet over medium-high heat. Add the ground beef and cook, breaking it apart, until well browned, 6 to 8 minutes. Drain the excess fat, leaving about 1 tablespoon in the pan.
Add the olive oil, onion, diced green pepper, and garlic. Cook until softened and translucent, 4 to 5 minutes.
Add the cumin, oregano, cinnamon, salt, and pepper. Stir for 30 seconds to bloom the spices.
Stir in the tomato paste and cook 1 minute, until it darkens slightly.
Add the tomato sauce, wine or stock, bay leaves, olives, raisins, and capers. Reduce heat and simmer uncovered for 10 to 12 minutes, until thick enough to mound on a spoon with no liquid pooling. Remove the bay leaves. Taste and adjust salt.
Preheat the air fryer to 360°F for 3 to 5 minutes.
Pack the picadillo into each pepper, mounding slightly. Brush the outside of each pepper with olive oil.
Stand the peppers upright in the air fryer basket with space between them. Air fry at 360°F for 15 to 18 minutes, until tender and lightly charred. Work in batches if they don't fit in a single layer.
If using cheese, add it during the last 3 minutes of cooking.
Let rest 5 minutes. Garnish with cilantro and serve over white rice if desired.