In a small saucepan, combine rice, ¾ cup water, and a large pinch of salt. Bring to a boil over medium-high heat. Cover and reduce heat to low. Simmer until rice is tender and water is absorbed, about 17 minutes.

Meanwhile, place a rack in upper third of oven; heat broiler on high. On a large baking sheet, toss poblano peppers with 1 tablespoon oil, then arrange cut side down. Broil, watching closely, until just starting to char in places, about 5 minutes. Turn peppers cut side up and continue to broil until crisp-tender, about 2 minutes more. Let cool slightly.

Preheat oven to 400°. In a large skillet over medium-high heat, heat remaining 1 tablespoon oil. Add beef, onion, and garlic; season with salt and pepper. Cook, stirring occasionally, until beef is cooked through and browned, about 7 minutes.

Add chipotle chile, tomato paste, oregano, and cumin and cook, stirring, until fragrant, about 1 minute. Add tomatoes and stir to combine. Bring to a boil, then reduce heat to medium-low and simmer, stirring occasionally, until liquid has slightly reduced, about 5 minutes.

Fluff rice with a fork and stir into beef mixture along with cilantro. In a 13" x 9" baking dish, arrange peppers cut side up; season with salt and pepper. Generously stuff each pepper with beef mixture. Top with cheese. Tightly cover baking dish with foil.

Bake stuffed peppers until tender, about 25 minutes. Uncover and switch oven to broil. Broil, watching closely, until cheese is bubbly, 2 to 3 minutes more.

Arrange peppers on a platter. Top with more cilantro.