In a large dutch oven, heat olive oil over medium high heat. Sprinkle chicken thighs with ½ teaspoon Kosher salt, then place into oil, skin side down. Cook until skin is nicely browned, about 5-6 minutes, then flip and brown on other side for an additional 5 minutes. Transfer to plate.
Add leeks to pot and let soften for about 5 minutes. Stir in mushrooms and 1 teaspoon Kosher salt. Cook, stirring occasionally, until mushrooms release their juices, about 10 minutes.
In a medium sized bowl, whisk together crème fraîche, chicken broth, and mustard. Add mixture to vegetables and stir. Reduce heat and let simmer for about 5 minutes.
Add chicken thighs back into vegetables, coating them with some of the sauce. Cover and cook for about 10-15 minutes, until chicken is cooked through. Let cool slightly to allow sauce to thicken.