Process walnuts in a food processor until finely ground. Place ground walnuts in a bowl. Process portobellos in a food processor until chopped. Add butter; process just until combined. Add mushroom mixture, freekeh, oats, beet, mayonnaise, soy sauce, salt, pepper, and garlic to ground walnuts; mix thoroughly to combine. Chill 1 hour.
Shape mixture into 10 (1/2-inch- thick) patties. Heat a grill pan over high. Coat with cooking spray. Cook patties until heated through and lightly charred, about 3 minutes per side. Remove from pan, and serve on buns with your favorite burger toppings.