Rinse beets under cold running water and cut in half or, if very large, in quarters. Beet juice can tint your skin pink, so wear kitchen gloves or just wash your hands well afterward. If any pink tint remains, a paper towel moistened with lemon juice will quickly remove it.
Place a steamer rack in the bottom of your pot, add 2-3 inches of water to the pot and bring to a rolling boil. Add beets, cover, and steam for 15 minutes. Remove from the heat, cover the pot, and let cool. The beets will cook a bit more while cooling.
While beets are steaming and cooling, prepare the apples and scallions.
Rinse both under cold running water. Cut the apples in half, remove & discard the core, place the cut side of the apple down on your cutting board, and slice lengthwise, then crosswise, so you end up with bite-sized pieces. Transfer to a large glass or ceramic (not plastic!*) bowl and add the lemon juice; this will both flavor the apples, add some vitamin C, and keep them from turning brown. (*Toxic compounds leach from plastic into food, particularly when acidic components like lemon juice or vinegar and/or fats, like olive oil or cheese, are present.)
Trim the root end from the scallions, slip off the outermost skin, then slice the scallion into small pieces and add them to the bowl with the apples. By now, your beets should be cool enough to handle easily. Wearing your kitchen gloves, transfer the beets to your cutting board and gently slip off their skin with your fingers. Discard the skin. Place the beets flat side down and cut, first lengthwise, then crosswise, for bite-sized pieces. Add the beets to the bowl with your apples and scallions.
Toss the apples and beets with balsamic vinegar till well distributed, then add the olive oil and toss again to coat the beets and apples well. Taste and add more balsamic and/or olive oil if desired.
Toss the walnuts with 1 teaspoon gluten-free Tamari—if desired – spread them over a baking pan and toast in your toaster oven or in your oven. If using the oven, set it to roast at 250 degrees for 5-10 minutes. Or you can toast the walnuts in a frying pan over medium heat, stirring them frequently. Your frying pan should be stainless steel or iron, not non-stick. Non-stick pans emit fumes containing toxic chemicals when heated.
Regardless of the method chosen, watch your walnuts as they can burn easily. (I speak from sad experiences here!) As soon as the walnuts’ color deepens, and you can smell their lovely nutty aroma, your walnuts are ready. Toast extra walnuts while you’re at it and save them in a glass storage container in the refrigerator (not plastic!) to add to salads, granola, yogurt and fruit, etc., or for a heart-healthy snack.
Crumble the feta cheese and sprinkle over the beet-apple mixture, then top with the toasted walnuts. Garnish with a few sprigs of Italian parsley, if desired, and serve.