Arrange chicken breasts on a cutting board and flatten the thicker part to an even thickness, sprinkle both sides with salt, pepper, and dust lightly with flour.
To toast the garlic, heat the olive oil in a medium sized skillet over medium-low heat. Once the oil is warm, add the garlic; cook over medium-low heat until light-golden brown, about 2 minutes. Remove the garlic with a slotted spoon and reserve on a plate, leave remaining oil in skillet.
In the same skillet with the remaining oil from toasting the garlic, cook chicken over medium heat, turning once, about 4 minutes on each side until chicken is 160°F with an instant read thermometer. Remove chicken from skillet and reserve on a platter.
For the sauce, heat butter in the same skillet over medium-low heat until melted, then add the onions. Cook onions until soft, about 4 minutes. Sprinkle the flour over the onions and continue to cook over low heat, stirring constantly until flour is incorporated into the butter, about 30 seconds. While stirring, gradually add chicken stock and continue cooking until sauce will begin to thicken, about 5 minutes.
Stir in mustards, toasted garlic, and half & half into the sauce, stir to incorporate. Add salt and pepper, to taste.
Add chicken and accumulated juices from the platter into the sauce and simmer for 2-3 minutes
Garnish with fresh parsley and serve immediately.
If chicken breasts are especially thick on one end, use a mallet or rolling pin to flatten thicker end so it cooks evenly.