Prepare the potatoes: Heat the oil in a 6-quart dutch oven over medium heat. Add the potatoes, salt, and black pepper and mix to coat in the pot. Cover, reduce heat to low, and cook until fork tender, 28 to 32 minutes. Remove from heat and toss with the dill, lemon juice, and 2 teaspoons lemon zest. Set aside and keep warm in the pot.

While the potatoes cook, prepare the chicken: Add the tapioca flour to a plate or shallow bowl. Pat the thinly sliced chicken dry with paper towels and season both sides with a sprinkle of salt and ground black pepper. Dredge the chicken in the flour, shaking off any excess and place on a plate. Repeat with the remaining cutlets.

Heat the olive oil in a large oven-safe skillet over medium-high heat. Once the oil is shimmering, carefully add the chicken working in batches, if necessary, so as to not overcrowd the pan. Cook until lightly browned and 165F internally, about 4 minutes per side, add additional oil as needed for cooking. Transfer to a clean plate, leaving the remaining oil behind in the skillet. Set the oven rack at least 3 inches from the broiler and pre-heat the broiler to high.

Add the asparagus, peas, and garlic to the same skillet. Cook, stirring often, until the asparagus has softened slightly, 2 to 3 minutes. Season with a couple generous pinches of salt.

Turn off the heat, stir the broth, yogurt, ricotta, lemon juice, and 2 teaspoons of zest into the mixture (note: you do not want the yogurt to come to a boil, do this step quickly to prevent separation. If swapping for coconut milk, this is not an issue). Return the chicken to the skillet on top of the vegetables. Top with the mozzarella cheese.

Transfer to the oven and broil until the cheese is melted and golden brown, 3 to 5 minutes. Divide the chicken and potatoes among 4 plates and spoon the sauce over top. Garnish with chopped parsley.