Add green beans to the pan; cook over medium heat, stirring occasionally, until lightly charred but still crisp, about 3 minutes. Transfer the beans to the plate with the chicken. Add oil to the pan; heat over medium-high heat. Add mushrooms, thyme and the remaining 1/4 teaspoon each salt and pepper. Cook, stirring occasionally, until the mushrooms are tender and lightly browned, about 4 minutes. Add cream and blue cheese; bring to a simmer over medium-high heat, stirring occasionally. Remove from heat; add the green beans and nestle them in an even layer in the sauce. Place the chicken on top of the beans.