Melt the butter in a skillet over medium-high heat. Whisk in the flour and cook, whisking constantly, until golden and bubbly, about 2–3 minutes.
Slowly whisk the chicken broth into the flour mixture until smooth. Bring to a boil, then reduce heat to medium-low and simmer for 5 minutes to thicken.
Remove the skillet from heat and stir in the sour cream, cumin, salt, garlic powder, and black pepper until combined.
Carefully transfer the warm sauce to a blender or food processor. Add the peeled and pitted avocados, 1/2 cup chopped cilantro, and lime juice. Pulse to a smooth cream, venting the lid occasionally to release steam. Taste and adjust seasoning if needed.
Preheat the oven to 350°F (175°C).
In a large skillet, heat the olive oil over medium-high heat. Add the sliced onion, sliced poblanos, and diced jalapeño and sauté until the onion is translucent, about 5–6 minutes. Remove from heat.
Assemble the enchiladas: lay a tortilla flat, spread 1–2 tablespoons of the avocado cream down the center, then top with some sautéed vegetables, shredded chicken, and a sprinkle of Monterey Jack. Roll tightly and place seam-side down in a 9x13 baking dish. Repeat with remaining tortillas.
Drizzle about half of the remaining avocado cream over the filled tortillas. Cover the dish with foil and bake at 350°F for about 20 minutes, until heated through and tortillas begin to firm.
Remove foil and garnish with additional cilantro, chopped red onion, and crumbled feta or extra cheese as desired before serving.