Prepare Components : In a small bowl, whisk together the arrowroot powder and 3 tablespoons of cool water to form a smooth slurry; set aside. In a separate bowl, combine the vegetable broth, lemon juice, and lemon zest. On your cutting board, pat the chicken pieces dry with a paper towel and season them evenly with the kosher salt and black pepper.
Sear the Chicken : Place the sauté pan over medium-high heat and add 1 tablespoon of olive oil. Once the oil shimmers, carefully add the seasoned chicken to the pan in a single layer, working in two batches if necessary to avoid crowding. Sear for 2–3 minutes per side until deeply golden but not fully cooked. Transfer the seared chicken to a clean plate.
Sauté the Vegetables : Reduce the heat to medium. Add the remaining ½ tablespoon of olive oil to the same pan. Add the shallot and cook for 2 minutes until softened. Add the asparagus pieces and sauté for 5–6 minutes, until vibrant green and tender-crisp. Stir in the minced garlic and optional red pepper flakes, cooking for another 60 seconds until fragrant.
Build the Pan Sauce : Pour the broth and lemon mixture into the pan. As it comes to a boil, use a wooden spoon or spatula to scrape up any flavorful browned bits (fond) from the bottom of the pan. Stir in the rinsed capers.
Simmer and Combine : Return the seared chicken and any accumulated juices to the skillet. Reduce the heat to maintain a steady, gentle simmer. Cook, stirring occasionally, for 5–7 minutes, or until the chicken is cooked through and the thickest piece registers 165°F (74°C) on an instant-read thermometer.
Thicken and Garnish : Give the arrowroot slurry a quick re-whisk and pour it into the simmering sauce. Stir constantly for about 1 minute as the sauce thickens to a glossy consistency. Remove the pan from the heat and stir in the fresh dill. Garnish with an extra sprinkle of dill and serve immediately.