Grind walnuts in blender or food processor, then mix with the rest of the burger mixture ingredients: oats, breadcrumbs, eggs, milk, onion, garlic, sage, and salt/pepper. Place the mixture in the refrigerator for about an hour to let the flavors come together and thicken slightly.
Place a skillet over medium heat and add in just enough oil to make a thin layer. Form the patties, then lightly fry for 2-3 minutes per side until golden brown. Once patties are brown, add the vegetable broth to cover the patties, then bring to a boil. Reduce heat to low and simmer, covered, for 20 minutes.
I love these most with fresh tomato slices, lettuce, pickled and spicy mustard!