Prepare the liver by carefully removing the outer membrane and trimming away any veins or tubes.
Place the liver slices in a bowl and pour the milk or buttermilk over them. Let soak for 30 to 60 minutes to neutralize the strong, metallic flavor.
Remove the liver from the milk, discard the soaking liquid, and thoroughly pat the slices dry with paper towels.
In a shallow dish, whisk together the flour, smoked paprika, salt, and pepper. Lightly dredge the liver slices in the flour mixture, shaking off any excess.
Heat 2 tablespoons of butter, olive oil, or beef tallow in a large skillet over medium-high heat. Add the sliced onions and cook until deeply caramelized. Add the garlic in the last minute of cooking, then remove the mixture from the skillet and set aside.
Add the remaining 1 tablespoon of fat to the hot skillet. Sear the liver slices very quickly, about 1 to 3 minutes per side. Do not overcook; they should remain slightly pink in the center to prevent a chalky texture.
Pour the beef broth into the skillet to deglaze the pan, scraping up any browned bits. Stir in the heavy cream and simmer for 1 minute.
Return the caramelized onions and garlic to the pan, tossing gently with the liver and sauce. Serve immediately.