Heat the olive oil in a large pot over medium heat. Add the onion and garlic to the pot and sauté until the onions have softened, around 5-8 minutes.
Stir in the green beans, tossing them well to coat them with the oil and aromatics. Sprinkle the all-purpose flour over the green beans and stir to distribute it evenly. Cook for about a minute, until you can no longer see the flour.
Pour the chicken broth into the pot and stir. Add the cajun seasoning, kosher salt, ground black pepper, and smoked paprika, adjusting the salt to your taste. Stir.
Bring the mixture to a simmer, then reduce the heat to medium-low. Cover the pot and let the green beans cook until tender, about 45 minutes to 1 hour.
Remove the lid and stir in the apple cider vinegar. If the sauce is too thin, let it simmer uncovered for a few more minutes to reduce and thicken to your liking.
Serve and enjoy.
Notes
The longer the beans cook, the softer they will become. If you cook them too long, they will become mushy.
I use kosher salt in this recipe. If using table salt, cut the amount in half and add as much salt as you prefer.