Heat oil in a large skillet. Add chicken breasts and cook over medium-high heat, turning once, until lightly browned, 2 to 3 minutes per side. Transfer chicken to a plate and set aside.
Add onion and garlic to skillet. Reduce heat. If necessary, add 1 to 2 tablespoons chicken broth. (If the pan appears too dry.) Cook until onion is translucent, about 3 minutes.
Add the remaining chicken broth and bring to a boil. Stir in mustard until blended.
Return chicken along with any juices on plate to skillet. Reduce heat to low, cover, and simmer 12 to 15 minutes, turning chicken once or twice until white throughout but still moist.
Transfer Chicken to a heated platter and cover to keep it warm.
Boil sauce in skillet 2 to 3 minutes to reduce slightly.
Put yogurt in a small bowl and gradually whisk in 1/3 cup hot sauce.
Stir yogurt mixture into sauce in skillet. Simmer until hot, about 1 minute. (Do not allow the sauce to boil to prevent the yogurt from curdling.)
Season with salt and pepper.
Pour sauce over chicken and serve with steamed zucchini or spinach.