Season the chicken breasts with paprika, salt, and pepper. Place in a shallow dish and add 2 tablespoons of the oil, 1 teaspoon of the mustard, the garlic, and half the lemon zest.
Toss until the chicken breasts are fully coated, then cover the dish and marinate at least 30 minutes, up to overnight.
On a baking sheet, toss the potato halves with 1 tablespoon of the olive oil. Season with salt and pepper and roast until tender and golden, 25 to 30 minutes.
Heat 1 tablespoon of oil in a large skillet over medium-high. Remove the chicken breasts from the marinade, and working in two batches, cook until golden brown on one side, 6 to 8 minutes. Flip each breast and continue to cook until the chicken is cooked through, 2 to 4 minutes longer. Transfer to a serving platter and repeat with the remaining oil and breasts.
In a small bowl, stir together the yogurt with the remaining 1 teaspoon mustard, lemon zest, salt, pepper and the parsley.
Serve the chicken with the yogurt and potato wedges.