Heat the oil in a large, heavy pot over medium-high heat until shimmering. Add the onion
and poblano and season with salt and pepper. Cook until the vegetables are softened, 3 to 5 minutes. Add the garlic and smoked paprika. Cook until fragrant, 45 to 60 seconds. Add the wine and cook until almost dry, 3 to 5 minutes.
Add the potatoes, stock, tomatoes with juice, butter beans, corn, and bouquet garni. Bring to a boil. Decrease the heat to simmer
. Cook, uncovered, until the butter beans and potatoes are just tender, about 30 minutes. Season the chicken and pork on both sides. Add the seasoned meat and continue to cook until the juices of the chicken run clear when pierced with a fork, 5 to 7 minutes. Taste and adjust for seasoning with salt and pepper. Ladle into warmed serving bowls and serve immediately.