Measure the brown rice and 1 cup water; rinse rice briefly. Peel and dice the sweet potato into small, even cubes. Dice the carrots and trim/chop the green beans.

Crack the egg into a small bowl and beat lightly. Measure the ground flaxseed, canned pumpkin, and dried parsley so everything is ready to add.

In a small saucepan, combine the rinsed brown rice and 1 cup water. Bring to a gentle boil, reduce heat to low, cover and simmer 25 minutes until tender; remove from heat and let rest covered for 5 minutes.

While the rice cooks, place a large skillet over medium heat and add the olive oil. Add the diced sweet potato and carrots; sauté for about 6–8 minutes, stirring occasionally, until they begin to soften.

Add the chopped green beans to the skillet and continue cooking 3–4 minutes until all vegetables are tender but not mushy. Transfer vegetables to a bowl and set aside to cool slightly.

Using the same skillet over medium heat, add the lean ground beef and break it apart with a spatula. Cook until no longer pink, about 6–8 minutes, draining any excess fat with a paper towel if there is more than a tablespoon.

Turn the heat off and add the cooked rice, sautéed vegetables, beaten egg, ground flaxseed, canned pumpkin, and dried parsley to the skillet with the beef. Stir thoroughly to combine; the residual heat will gently cook the egg and bind the mixture.

Allow the mixture to cool completely to lukewarm before serving. Divide into portions appropriate for your dog's size and refrigerate any leftovers within 2 hours.