Step 1
Preheat the oven to 350 degrees F (175 degrees C).
Step 2
Cut each chicken thigh into 5 or 6 pieces. Lightly season with salt and pepper.
Step 3
Heat oil and butter in a 6-quart oven-safe Dutch oven over medium-high heat until hot. Add chicken pieces and cook until lightly browned but not cooked through about 2 minutes per side. Remove chicken from the pot with a slotted spoon and set aside.
Step 4
Add onions to the hot pot; cook and stir for 1 minute. Add carrots and celery; cook stirring occasionally for 1 more minute. Add mushrooms and cook for 1 minute. Add green beans and garlic; cook and stir until fragrant about 2 minutes. Season lightly with salt and pepper to taste.
Step 5
Pour wine into the pot and bring to a boil while scraping the browned bits of food off the bottom of the pan with a wooden spoon. Add chicken and any accumulated juices back to the pot. Pour in just enough chicken broth to barely cover everything in the pot. Sample broth and adjust seasonings if necessary. Add rosemary sprigs pressing them below the surface of the liquid.
Step 6
Cover and place in the center of the preheated oven. Bake until vegetables are tender and chicken is no longer pink in the center and the juices run clear about 30 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C). Remove rosemary sprigs.
Step 7
Place cornstarch in a small bowl and add just enough water to create a thin paste. Stir until all lumps are dissolved and slowly add to the stew stirring constantly.
Step 8
Place stew on the stove and heat over medium heat. Cook and stir until gravy has thickened and desired consistency has been achieved about 5 minutes.