Pre-heat the oven to 375°F. Trim any excess fat from the tops and sides of the chicken breasts.
With a heavy knife or poultry scissors, trim off the small side rib bones for a clean edge. Discard the ribs and excess fat.
Over medium heat, add olive oil to a 5½-quart Dutch oven or other heavy pan large enough to hold all of the chicken breasts in a single layer. Combine salt, garlic and pepper in a small bowl and sprinkle over the chicken breasts. Place the chicken breasts skin side down and allow them to cook until they have a golden brown crust, 5-7 minutes. Turn the chicken over.
In a bowl or large measuring cup, whisk together the broth, almond milk, cashew butter, mustard and the garlic until smooth. Pour around the chicken in the pan. Sprinkle with chopped thyme leaves. Place a lid on the pan and place in the oven. Roast the chicken for approximately 30 minutes or until a digital thermometer reads 160°F-165°F when inserted into the thickest part without touching the bone. When the chicken is done, remove the pieces to a plate or platter and keep it warm covered with foil.
In a small bowl or measuring cup, combine the water and the arrowroot starch and stir until smooth. Add the arrowroot mixture to the pot with the chicken juices and whisk until smooth. Simmer for 2-3 minutes to cook off the raw taste and for the juices to thicken into gravy.
Serve the chicken with a 1/2 cup of the gravy per person. Store any leftover sauce in an airtight container in the refrigerator up to 5 days.