Preheat your oven to 350°F (175°C).
In a twelve-inch skillet, combine the chopped poblano peppers, half of the chopped onions, 2 tsp coconut oil, and 0.25 tsp sea salt.
Cover the skillet and cook over medium-low heat until the vegetables are softened, about 8 to 10 minutes.
Uncover the skillet and increase the heat to medium-high.
Cook, stirring occasionally, until the vegetables are lightly browned, approximately 4 to 6 minutes.
Stir in 2 tbsp of the minced cilantro, the minced garlic, and the chipotle chilies.
Cook until fragrant, about 30 seconds.
Stir in the canned tomatoes with their juices and the 0.75 cup (6 oz / 180 ml) chicken broth.
Add the chicken breasts and bring the mixture to a simmer.
Reduce the heat to low, cover, and cook until the chicken registers 160°F (71°C), typically 10 to 15 minutes.
Transfer the chicken to a carving board and allow it to cool slightly.
Shred the chicken into bite-size pieces.
Transfer the remaining sauce from the skillet to a blender and process until smooth, about 1 minute. Return the sauce to the skillet, season with sea salt and pepper to taste, and bring to a simmer over medium heat.
Remove the skillet from the heat and stir in the shredded chicken.
Transfer the mixture to an eight-inch square baking dish and sprinkle the 3 oz (85 g) of crumbled cheese evenly over the top.
Bake on the lower-middle rack of the oven until hot throughout, roughly 5 to 10 minutes.
Allow the casserole to cool slightly.
In a small bowl, combine the 0.125 cup (1 oz / 30 ml) coconut milk and 1 tbsp lime juice.
Drizzle this mixture over the casserole.
Sprinkle with the chopped tomato, the remaining onions, and the remaining cilantro.
Serve warm.
Shredding Hack: If you own a stand mixer, place the warm chicken breasts in the bowl and run it with the paddle attachment on low speed. It shreds the chicken perfectly in seconds, saving you time and effort compared to using forks.
Sauce Safety: When blending the hot sauce mixture, always remove the center cap of the blender lid and cover the opening with a kitchen towel. This allows steam to escape and prevents the hot liquid from splattering or causing the lid to pop off.
Make-Ahead Friendly: You can prepare the chicken and sauce mixture up to a day in advance. Store it in the refrigerator, then assemble with the cheese and bake when you're ready to eat. If baking from cold, you may need to add 5–10 minutes to the baking time.
Customize the Heat: The spice level here comes mainly from the chipotle chilies. If you prefer a milder dish, start with 1 tsp and taste the sauce before adding more. For extra heat, feel free to add a pinch of cayenne or leave the seeds in if you substitute with fresh jalapeños.
Melting Dairy-Free Cheese: Since dairy-free cheeses often have a higher melting point than traditional cheddar, try switching the oven to "Broil" for the last 1–2 minutes of cooking. This helps achieve that bubbly, golden finish—just watch it closely to ensure it doesn't burn!