In a medium saucepan put 1 cup water and barley, cover and bring to a boil. Reduce heat to low and cook until liquid is completely absorbed, about 15 minutes, uncover the pan during the last minutes. Meanwhile in a small saucepan put 1 1/2 cup water, edamame and lentils, bring to a boil and cook until soft, about 15 minutes (strain if any juice is left after cooking, you want the mix completely dry). When all is ready, add edamame and lentils to the barley and mix, set aside to cool slightly.
In a food processor, pulse carrot, onion, garlic, and celery until finely chopped. Transfer this mix into a small pan with a tablespoon olive oil and toss for five minutes to warm up the vegetables and fully release the flavor of onion and garlic.
At this point you can form the patties. As I said this mixture will make about 12. If your mix is too soft, refrigerate 20 minutes to firm. How to proceed: slightly wet your hands with water and take enough mixture to form a 3/4″ thick and about 4″ diameter patty. Give it a rough round shape on your hand and then place it on a piece of parchment or wax paper on your working surface and flatten its top and edge to the desired shape. If you freeze the burgers, you can make little piles of three separated by squares of parchment paper.
To cook the patties heat one tablespoon olive oil over medium heat in a large nonstick skillet. Cook burgers until browned and cooked through, about 6-7 minutes per side. I topped my burgers with slices of asiago cheese, and had them with a light tomato hot sauce and a green salad with alfalfa sprouts and pickles.