Preheat oven to 375°F (190°C). Lightly grease a large casserole dish with cooking spray or oil and set aside.
Preheat a large pot over medium heat. Add butter, swirl to coat the bottom, then add onion and cook, stirring occasionally, until onion has softened, 2-3 minutes.
Add garlic, stir to combine, and cook for 1-2 minutes more, until fragrant.
Sprinkle onion mixture with flour and stir to coat. Slowly add broth, stirring constantly until fully combined and no flour lumps remain.
Add milk, nutmeg, salt, and pepper. Stir once more and bring to a simmer, then reduce heat and continue to cook, stirring occasionally, until mixture has thickened, 8-10 minutes.
Add chicken, beans, kale, and 1 cup (250 mL) of cheese. Continue to cook, stirring often, until kale has wilted, 2-3 minutes. Remove from heat and transfer mixture to the prepared casserole dish.
Meanwhile, place remaining cheese, breadcrumbs, and oil in a small bowl. Stir well to combine.
Spread breadcrumb mixture evenly on top of the casserole. Bake in preheated oven until golden, about 30 minutes. Serve immediately and enjoy!