1. Place liver slices in a bowl and cover with milk. Let soak for 30–60 minutes in the refrigerator for best tenderness and flavor.

2. In a large skillet over medium heat, melt 2 tablespoons of butter with 1 tablespoon olive oil. Add the sliced onions and 1/2 teaspoon salt. Cook, stirring occasionally, for 20–25 minutes until onions are golden and caramelized. Transfer onions to a plate and keep warm.

3. Remove the liver from the milk and pat dry with paper towels. Season both sides with 1/2 teaspoon salt and 1/4 teaspoon pepper. Dredge each slice in flour, shaking off any excess.

4. Wipe the skillet clean, then add the remaining 2 tablespoons butter and 1 tablespoon olive oil over medium-high heat. When hot, add liver slices in a single layer (work in batches if needed). Sear for 1–2 minutes per side, until browned but still slightly pink in the center.

5. Return the caramelized onions to the skillet with the liver. Sprinkle with the remaining 1/4 teaspoon pepper. Toss gently and warm together for 1–2 minutes. Garnish with fresh thyme if desired and serve immediately.