Heat oil in a skillet over medium heat. Fry shallot and garlic in hot oil until golden brown, 2 to 3 minutes; add kale, cream of chicken soup, sriracha sauce, cream cheese, and sour cream to the skillet. Cook and stir the mixture until the cream cheese melts and the liquid is even in color, about 5 minutes.
Stir green beans into the mixture to coat, season with black pepper, reduce heat to medium-low, and simmer until the sauce thickens slightly, 5 to 7 minutes.