Heat butter and olive oil in a large pot over medium, then cook the onion, carrots, celery, garlic, paprika, and a big pinch of salt until softened.
Stir in the flour and cook briefly, then add the chicken broth and vinegar, stirring until smooth.
Add the chicken thighs, potatoes, green beans, cream, sage, thyme, oregano, salt, and pepper, bring to a gentle boil, then reduce to a simmer and cook partially covered until the chicken is cooked through, about 20 minutes.
Remove and shred the chicken, fully cover the pot and cook the vegetables until tender, then return the chicken, season to taste, and serve warm with parsley and lemon wedges if desired.
