To prepare the sage chimichurri sauce: Combine sage, olive oil, garlic, salt and lemon juice in blender and blend until smooth to create the chimichurri sauce.
Marinate liver in the chimichurri for 1–4 hours and reserve.
Brown liver in hot sauté pan until desired doneness; medium or still a little pink is perfect.
Butter the sourdough bread and grill it. Add 3 ounces cheese for each sandwich and melt. Remove from the grill and pile 4–5 ounces of cooked liver and 1 ounce grilled onions on each sandwich and serve.