Preheat oven to 400 degrees F. Line a large baking sheet with parchment paper and brush it with a little olive oil.
Rinse and dry the poblanos. Cut a thin slice off the tops and remove the core and seeds. Cut a slit down the side of each pepper. Set aside.
Heat the olive oil in a large, deep skillet over medium-high heat and brown ground beef. Add the tomatoes, onion, garlic, oregano, cumin and salt. Cook, stirring often, until liquids have evaporated, about 7 minutes. Off heat, stir in the hatch pepper cheese and the cilantro, mixing well.
Divide the filling among the peppers, adding it from the top and pressing on it to fill the entire pepper. Place the stuffed peppers on the prepared baking sheet. Bake 15-20 minutes, until the poblanos are soft and charred in places (the smell will be amazing!).
Remove the baking sheet from the oven and switch the oven to broil. Top the peppers with the cheddar cheese and broil just until the cheese is melted, about 2 minutes. Allow to rest 5 minutes before serving