Toss your chicken pieces in a bowl with half the cumin, the chili powder, salt, and pepper. Heat oil in your Dutch oven until it's glistening, then add the chicken in batches so it doesn't steam. Cook it for 4-5 minutes until golden brown on both sides, then set it aside on a plate.
In that same pot, melt the butter and toss in your chopped onions. Cook for 2-3 minutes until they've softened up nicely. Stir in the garlic, oregano, and the rest of the cumin, letting it cook for about 30 seconds until it's fragrant and your kitchen smells incredible.
Sprinkle the flour directly into the pot and stir constantly for about a minute. This step is what gives the chili its signature creamy body, so don't skip it or rush through it. It should look like a light, pale paste coating the onions before you move forward.
Add in the chiles, beans, broth, and your browned chicken back into the pot. Season with a bit more salt and pepper, then bring it to a simmer. Cover it partially and let it cook on medium-low for 20 minutes, stirring occasionally so nothing sticks to the bottom.
Once the chili has thickened up and the chicken is fully cooked through, stir in the heavy cream. Let it simmer for another 1-2 minutes until everything turns silky and rich. Give it a final taste and adjust the salt if needed before turning off the heat.
While the chili simmers, bring water and rice to a boil in a separate saucepan, then reduce to a simmer until the water's absorbed. Fluff it with a fork and spoon it into bowls. Ladle the chili generously over the rice, then top with pico de gallo and green onions.