Preheat oven to 300°F. Line a baking sheet with parchment paper or aluminum foil. Place a wire rack on top of the lined baking sheet.
Cut slits in the fat of the duck breasts. Place the duck breasts, skin side down on the wire rack. Bake for 2 hours or until the internal temperature reaches 165°F.
While the duck is baking, prepare the barley mixture. Place the water, barley, carrots, and rosemary in a saucepan. Bring to a boil over high heat then reduce heat to low. Loosely cover with a lid allowing it to vent. Cook on low for 20 minutes.
Remove the pan from the heat, tightly cover it with the lid, and let sit for 20 minutes or until the barley has absorbed all the water. Stir in the green peas.
When the duck has finished cooking, cut the meat into small bite-sized pieces and stir the meat into the barley mixture.
Allow the food to cool to room temperature before serving it to your dog.
Store the food in an airtight container in the refrigerator for up to 4 days. Freeze it for up to 3 months.