Gather and prepare all your ingredients. Slice the onion into thin rings (about ¼ inch or less) and finely mince the garlic.
Slice the liver into pieces about ¼–½ inch thick, trimming off any silverskin if needed. Rinse the slices under cool water to remove excess blood, then place them in a bowl and cover with milk, or with cool water mixed with the juice of half a lemon. Cover and refrigerate for at least 30 minutes, or up to overnight. If soaking longer, change the milk or water once it becomes very bloody.
After soaking, drain the liver and pat it completely dry with paper towels or a clean cloth. Transfer to a bowl and season with ½ teaspoon salt, ¼ teaspoon black pepper, and ¼ teaspoon dried sage (or rosemary or thyme). Toss gently to coat evenly.
Melt 1 tablespoon of your chosen cooking fat in a skillet over medium-high heat. Add the minced garlic and onion rings with a generous pinch of salt. Sauté for about 5 minutes, stirring often, until the onions begin to soften and turn golden. Remove the onions from the pan and set aside.
In the same pan, melt the remaining tablespoon of fat. Once hot, add the liver slices in a single layer, working in batches if needed to avoid overcrowding.
Cook the liver for about 1 to 1½ minutes per side, depending on thickness. The outside should be nicely browned, while the inside remains slightly pink and tender. Avoid overcooking as it can turn tough and rubbery quickly.
Remove the liver from the pan. Return the onions to the skillet and warm them for a minute or two. Then add the liver back in, toss everything together, and garnish with fresh chopped parsley if you like. Serve warm, with a lemon wedges for brightness.