Put the cilantro, chiles, sweet peppers, lime juice, and a good pinch of salt in a mini food processor and pulse to finely mince (or use a chef’s knife and mince the cilantro, chiles, and peppers together on a cutting board, then transfer to a bowl and stir in the lime and salt). Cover and refrigerate if doing this in the morning.
Heat a large nonstick pan or griddle over medium heat. When a drop of water on the surface evaporates almost instantly, add the cheese slices in a single layer (in batches if necessary) and cook without disturbing them until nicely browned, 1 to 2 minutes. Flip with a thin spatula and brown the other side. Serve the cheese topped with the chile mince.