Preheat your broiler to high. Rub the poblano peppers with olive oil and place them on a foil-lined baking sheet. Broil for 5-7 minutes, turning occasionally, until lightly blistered but not completely blackened.

While the peppers cool slightly, mix the softened cream cheese, half of the Monterey Jack cheese (1/2 cup), cumin, salt, and black pepper in a bowl until it forms a thick, uniform paste.

Make a single lengthwise slit down each cooled poblano. Carefully remove the seeds. Generously stuff each pepper with the cream cheese mixture and gently press the edges together.

Lower the oven to 375°F (190°C). Place the stuffed peppers in a ceramic baking dish. Top generously with the remaining Monterey Jack and the sharp cheddar cheese. Bake for 15-20 minutes until the cheese is bubbly and golden brown.

Remove from the oven and let rest for 5 minutes. Garnish with fresh chopped cilantro before serving.