Make the pistou: Blend 1 cups frozen peas, thawed, ½ cup fresh basil leaves, 3 tablespoons olive oil and 1 tablespoons lemon juice until smooth. Season with salt. Set aside at room temp, it will sit happily while you cook everything else.
Warm your stock: Pour 5 ½ cups warm chicken stock into a small saucepan over low heat and keep it warm throughout. Never add cold stock to risotto.
Sear the chicken: Pat 4 boneless skinless chicken thighs dry and season all over with salt and pepper. Heat 2 tablespoon of 3 tablespoons olive oil, divided in a wide, heavy-bottomed pan over medium-high heat. Sear the chicken 4–9 minutes per side until deep golden and cooked through. Transfer to a cutting board to rest.
Build the base: Reduce heat to medium. Add remaining 1 tablespoon of 3 tablespoons olive oil, divided to the same pan. Add 3 garlic cloves, minced and 14 ounces jarred artichoke hearts, drained and roughly chopped and cook 2 minutes more, scraping up any browned bits from the chicken as you stir.
Toast the rice: Add 1 ½ cups Arborio rice and stir to coat in the oil. Toast for 2 minutes stirring constantly, until the edges of the grains look slightly translucent.
Add stock and stir: Add your warm stock about ½ cup at a time, stirring often and waiting until each addition is mostly absorbed before adding the next. Keep the heat at a gentle simmer. This takes about 18–20 minutes total.
Slice the chicken and finish the risotto: While the last ladle of stock absorbs, slice or shred your rested 4 boneless skinless chicken thighs.
Remove the pan from heat. Stir in 3 tablespoons unsalted butter and a generous amount of Parmigiano-Reggiano, finely grated vigorously until creamy and glossy. Nestle the sliced chicken into the risotto to warm through. Season generously with 1 pinch kosher salt and black pepper.
Plate and serve: Spoon into wide bowls, drizzle the pistou generously over the top, and finish with shaved parm. Serve immediately.