Pat the chicken dry and season with 1 teaspoon of kosher salt per pound of chicken and ½ teaspoon of black pepper per pound of chicken.
Heat 1 tablespoon extra virgin olive oil over medium heat in a skillet. Once hot, add the chicken–in batches if needed–and cook without moving for 5 minutes. Flip and cook for an additional 1 to 2 minutes. Transfer the chicken to a plate and leave the skillet on medium.
Sauté the mushrooms and leeks:
Add the sliced mushrooms to the hot skillet and cook for 6 to 8 minutes to allow the water to cook off the mushrooms. Once the moisture in the skillet evaporates, add 2 teaspoons extra virgin olive oil and a pinch of salt and pepper.
Add the sliced onion and leeks to the mushrooms and cook for 10 to 12 minutes, stirring regularly until softened. Taste and season with salt and pepper.
Add the champagne vinegar and the chicken stock to the skillet and bring to a boil. Cook for 3 to 4 minutes. Remove from heat.
Braise the chicken:
Transfer the vegetable mixture to a large baking dish or roasting pan. Arrange the chicken legs, skin-side up, on top of the vegetables. Add the thyme sprigs on top of the chicken.
Transfer to the oven and cook, uncovered, for 45 minutes or until an instant-read thermometer reaches 165ºF in the thickest part of the chicken leg.
Finish the sauce:
Remove the baking dish from the oven but leave the oven at 400ºF. Remove and discard the spent thyme sprigs. Transfer the cooked chicken legs to a plate.
Add crème fraîche and frozen peas to the sauce and whisk until the crème fraîche melts. Add a pinch of salt and pepper. Transfer to the oven for 5 minutes to cook the peas.
Remove from the oven. You can skim off any excess chicken fat from the top of the sauce and discard it if you prefer. Taste the sauce and season with more salt and pepper if needed.
To serve:
Arrange the cooked chicken on top of the sauce. Garnish with a few fresh thyme leaves. Enjoy!