Adjust oven rack to upper-middle position and heat oven to 450 degrees. Heat oil in 12-inch nonstick skillet over medium heat until shimmering. Add onion and cook until softened, about 5 minutes. Stir in beef, breaking up meat with wooden spoon, and cook until no longer pink, 8 to 10 minutes. Using slotted spoon, transfer beef mixture to paper towel-lined plate. Pour off all but 2 tablespoons fat from skillet.

Add poblanos to fat left in skillet and cook over medium-high heat until browned, 8 to 10 minutes. Stir in garlic, cumin, oregano, cayenne, ¼ teaspoon salt, and ½ teaspoon pepper, and beef mixture and cook until fragrant, about 30 seconds. Stir in tomatoes and cook until mixture is dry, about 1 minute. Off heat, stir in 2 cups Monterey Jack. Transfer mixture to 13 by 9-inch baking dish and press into even layer.

Combine flour, ½ teaspoon salt, and ¼ teaspoon pepper in bowl. Slowly whisk in milk until smooth. Using stand mixer fitted with whisk attachment, whip egg whites on medium-low speed until foamy, about 1 minute. Increase speed to medium-high and whip until stiff peaks form, about 3 minutes. Whisk one-third of whipped egg whites into milk-flour batter to lighten. Gently fold in remaining whites, 1 scoop at a time, until combined.

Pour batter evenly over beef mixture. Bake until topping is light golden and puffed, about 15 minutes. Sprinkle with remaining ½ cup Monterey Jack and bake until golden brown, about 10 minutes. Let cool on wire rack for 10 minutes. Serve.