Finely grind walnuts. Place ground walnuts, chopped portobello mushrooms, softened butter, rice flour, oats, beets, mayonnaise, soy sauce, and Holy Mo'ly seasoning in a bowl. Mix thoroughly to combine.
Shape mixture into (1/2-inch- thick) patties. Heat a grill pan or griddle on high. Add cooking oil or cooking spray. Cook patties until heated through and lightly charred, about 2 minutes per side. Remove from pan or griddle and place in oven safe pan covered with foil. Place in oven for 10 minutes to allow oats to soften. Remove and serve on buns with your favorite burger toppings.