In a large pot, melt 2 tablespoons of salted butter over medium heat. Add 1 chopped yellow onion and 3 minced garlic cloves, sautéing until translucent and fragrant, about 5 minutes. Stir in 1 tablespoon of chopped fresh oregano and 1 teaspoon of chili powder. Season with salt and black pepper to taste.

Whisk in 1/4 cup of all-purpose flour and cook for another 2 minutes, stirring constantly until a roux forms.

Pour in 4 cups of bone broth, stirring to avoid lumps. Add 3 peeled and diced russet potatoes and 2 cups of chopped broccoli, bring to a simmer. Cover partially and cook for 15-20 minutes until potatoes are fork-tender.

Mash some of the potatoes and broccoli directly in the pot for a chunky texture or carefully blend for a smoother consistency.

Lower the heat and stir in 1 cup of milk, 1/2 cup of salsa verde, and 1 1/2 cups of shredded cheddar cheese until melted and creamy. Taste and adjust seasoning as needed.

Ladle soup into bowls and garnish with chopped green onions and additional cheddar cheese. Serve immediately.