Preheat oven to 425° Place quartered potatoes in a large bowl. Add olive oil and dried rosemary and season with kosher salt and pepper. Arrange in a single layer on a rimmed baking sheet. Roast for 30-40 minutes until potatoes are browned and crispy on the outside and tender on the inside. Stir once about halfway through cooking.
Meanwhile, prepared the chicken. Pat chicken dry with a paper towel. Season with salt and pepper. Put flour in a dish and dip chicken in the flour to cover, shaking off the excess.
Add 1 ½ tbsp. of the avocado oil to a large skillet over medium heat. When the oil is hot, add half of the chicken and brown on both sides until the chicken is cooked through and reaches an internal temperature of 165° Remove the chicken to a plate and cover with foil to keep warm. Repeat with another 1 ½ tbsp. of avocado oil and the remaining chicken.
Add the remaining 1 tbsp. of oil to the empty skillet. Add shallot and cook until soft and translucent.
Stir in the chicken stock and bring to a simmer, being sure to scrape up any browned bits from the bottom of the pan. Simmer until it starts to thicken, about 10 minutes.
While the sauce is thickening, prepare the green beans. Add 1 tbsp. of olive oil to a skillet over medium heat. Add trimmed green beans to the skillet and season with salt and pepper. Cook to your desired level of tenderness. Turn off the heat and add the butter.
Turn off the heat for the sauce and stir in the dill, mustard, and butter. Taste the sauce for seasoning and adjust accordingly.
To serve, plate chicken and spoon sauce over top. Serve with the roasted potatoes and green beans.