In a large heavy pot over medium heat, heat the oil and butter. Add onion and sauté just until the onion is softened, stirring occasionally. Add the green curry paste and the yellow curry paste, and stir to combine. Then add the garlic, ginger, red bell pepper, and mushrooms, and stir to combine. Cook until vegetables are softened, about 5 minutes, stirring occasionally.
Add chicken broth, coconut milk, fish sauce, brown sugar, red pepper flakes, and chicken. Stir to combine and cook until thoroughly warmed.
Before serving, stir in lime juice, green onions, and cilantro. Season with kosher salt and freshly cracked black pepper, to taste. Offer additional lime wedges to squeeze over the top of individual bowls, if desired.