Preheat the oven to 400°F (200°C). Pat chicken thighs with paper towel, then season with salt and pepper. Place chicken thighs chicken skin side down in a cast-iron skillet or dutch oven to render the skin. Cook thighs until you get that golden brown crispy skin, about 15-20 minutes on med-high heat. Transfer chicken skin-side up to a plate.
Add shallots and leeks, cut side down, to the pan. Cook until charred, about 2-3 minutes. Then, add asparagus and toss all vegetables with a wooden spoon. Season with salt and a pinch of pepper.
Return the chicken thighs to the pan in a single layer, skin side up, and transfer to the oven. Bake for 15-20 minutes, or until the internal temperature of the chicken reaches 165°F (74°C).
Remove skillet from the oven and place back on the stove. Transfer the chicken from the pan into a plate and set aside, chicken skin-side up. Add fresh or frozen peas to the asparagus leek mixture and season with salt and pepper. Cook on medium heat for 2-3 minutes on med-high heat.
Stir in cold butter until the sauce emulsifies and scrape bottom of potto make sure you get the brown bits. Squeeze in lemon juice and mix in tarragon.
Place the chicken thighs back in the pan. Garnish with additional tarragon and serve.