Preheat the broiler and arrange poblano peppers on a sheet pan.

Broil the poblanos until charred on all sides, turning every few minutes (8-12 minutes total).

Transfer the poblanos to a bowl, cover tightly with plastic wrap, and let steam for 10 minutes.

Peel, seed, and chop the peppers, discarding the skin, stems, and seeds. Set aside.

Add ground beef to a large pot over medium-high heat and cook, stirring often, until browned (8-10 minutes).

Remove the ground beef with a slotted spoon and set aside, leaving the fat in the pan.

Add the leeks and cook, stirring occasionally, until softened (about 5 minutes).

Add the minced garlic and cook until fragrant.

Add the chopped poblanos, corn, and oregano and continue to cook until the corn is cooked through (about 5 minutes). Add a little olive oil if mixture seems dry.

Add the chicken stock and cream cheese and simmer until the cheese melts and the flavors meld (about 5 minutes more).

Stir in the heavy cream and the cooked ground beef.

Season to taste with salt and pepper.

Simmer until the soup is warmed through and serve immediately.

Top with shredded Monterey Jack cheese before serving.

Refrigerate any leftovers.