Begin by preparing the ancho chiles. Carefully make a slit down one side of each chile, from stem to tip, being careful not to cut all the way through. Remove the seeds and veins. You can toast them lightly in a dry skillet for about 30 seconds per side to enhance their flavor, then place them in a bowl and cover with hot water for about 20-30 minutes, or until softened. Drain and pat dry.
While the chiles are rehydrating, prepare the filling. Heat the olive oil in a large skillet over medium-high heat. Add the ground meat and cook, breaking it up with a spoon, until browned. Drain off any excess fat.
Add the chopped onion to the skillet with the meat and cook until softened, about 5 minutes. Stir in the minced garlic, cumin, smoked paprika, and cayenne pepper (if using). Cook for another minute until fragrant. Season generously with salt and pepper.
Stir in the drained diced tomatoes, cooked rice, and half of the shredded cheese. Mix well to combine. Remove from heat.
Preheat your oven to 375°F (190°C).
Carefully stuff the softened ancho chiles with the meat and rice mixture, dividing it evenly. Place the stuffed chiles seam-side up on a baking sheet.
Sprinkle the remaining shredded cheese over the top of each stuffed chile. You can add a small dollop of the tomato mixture on top of the cheese if desired.
Bake for 20-25 minutes, or until the cheese is melted and bubbly, and the chiles are heated through. If they start to brown too quickly, you can loosely tent them with foil.
Garnish with fresh cilantro and serve immediately with a dollop of sour cream or Greek yogurt.