1. Preheat oven to 375°F. Prepare and bake cornbread mix according to package directions, using 2 eggs, milk, and ½ cup vegetable oil. Cool completely; cut into 1-inch cubes and set aside. 
2. In a medium bowl, add chayote and chile peppers. Drizzle with ¼ cup lime juice; toss to coat. Let stand at room temperature for 10 minutes. Add remaining 2 Tbsp. vegetable oil and 2 Tbsp. agave nectar; toss to coat and set aside. 
3. Heat a 12-inch cast-iron skillet over high heat. Add chayote-chile peppers mixture to skillet. Cook for 5 to 7 minutes or until charred, turning frequently. Transfer to a bowl. Cool slightly; cut chile peppers into 1-inch pieces and return to bowl with chayote. Set aside.
4. Add chorizo to the cast-iron skillet. Cook over medium-high heat for 3 to 5 minutes or until chorizo reaches 165°F, stirring occasionally and breaking into large crumbles. Transfer to a bowl; cover to keep warm. Wipe skillet clean with paper towels. 
5. In a small bowl, whisk together remaining 3 eggs, broth, and oregano. In the cast-iron skillet, layer half each of cornbread cubes, chayote-chile mixture, chorizo, and egg mixture. Repeat layers. Cover skillet with foil.
6. Bake for 25 minutes. Uncover and bake for 10 to 15 minutes more or until vegetables are crisp-tender and cornbread is crisp. Garnish with additional agave, corn snacks, and cilantro, if desired. Serve with lime wedges.

*Chile peppers contain volatile oils that can burn your skin and eyes. When working with poblano chiles, wear protective gloves.