The leeks get silky when they cook down in this luscious, tangy mustard sauce. Serve over mashed potatoes.
Heat 1 tablespoon oil in a large pot over medium heat. Pat chicken dry and sprinkle with 1/4 teaspoon each salt and pepper. Add the chicken to the pot and cook until browned on both sides, 6 to 8 minutes total. Transfer to a clean plate.
Add the remaining 2 tablespoons oil and mushrooms to the pan and cook, stirring occasionally, until lightly browned, 4 to 6 minutes. Stir in leek and cook, stirring occasionally, until the leek is just starting to soften, about 4 minutes. Stir in garlic and thyme (or tarragon) and cook until fragrant, about 1 minute. Sprinkle the mixture with flour and cook, stirring, for 1 minute.
Add broth, increase heat to high and bring to a simmer, scraping up any browned bits. Adjust heat to maintain a low simmer. Return the chicken and any accumulated juices, cover and cook until an instant-read thermometer inserted in the thickest part of a thigh registers 165 degrees F, about 10 minutes. Season with the remaining 1/2 teaspoon salt and 1/4 teaspoon pepper.
Transfer the chicken to a serving platter. Add peas and mustard to the sauce and cook, uncovered, until the peas are heated through, about 2 minutes. Ladle the sauce over the chicken and garnish with more thyme (or tarragon), if desired.
Sun exposure triggers vitamin D production in mushrooms, making them one of the few food sources of this nutrient. Wild mushrooms have even more D than cultivated, which are usually grown in the dark.