Prepare the Squash: Preheat the oven to 350°F. Cut the tops off the cousa squash and use a spoon to carefully hollow out the centers. Dice the removed flesh into small pieces and set aside.
Pre-Bake: Place the hollowed squash into a baking dish. Drizzle with 1 tablespoon of olive oil and season with a portion of the salt and pepper. Bake for 10 minutes until just beginning to soften.
Sauté the Filling: In a large skillet over medium-high heat, add the remaining 2 tablespoons of olive oil. Sauté the diced squash flesh, eggplant, onion, and poblano pepper. Season with the remaining salt and pepper. Cook until tender and lightly browned (5 to 8 minutes).
Brown the Chorizo: Add the fresh chorizo to the skillet. Cook, crumbling the meat with your spoon, until browned (3 to 5 minutes).
Fold in Beans and Cheese: Stir in the white beans and grated cheddar until combined.
Stuff and Finish: Reduce oven heat to 300°F. Spoon the filling generously into the pre-baked squash boats. Bake for an additional 10 to 15 minutes until the squash is completely tender. Garnish with any extra filling around the sides.