Heat olive oil in a Dutch oven over medium-high heat. Season chicken thighs with salt and pepper, then brown them on both sides. Remove and set aside.
In the same pot, add onion, garlic, celery, and mushrooms. Cook until softened.
Add thyme and rosemary. Deglaze with white wine, letting it simmer and reduce.
Add the halved baby potatoes and chicken broth. Bring to a simmer. Return the chicken to the pot, cover, and simmer until the chicken is nearly cooked, about 30 minutes.
Add the heavy cream and frozen peas, cooking until the chicken and potatoes are fully tender and the sauce is creamy. Adjust salt and pepper to taste.
Sprinkle with fresh parsley before serving.
Notes
For a lighter version, you can use half-and-half instead of heavy cream.