Preheat oven to 400 degrees. Spray a 12-cup standard muffin tin with cooking spray; set aside. Cut 3 apple quarters into 1/4-inch dice; cut remaining apple quarter into 12 thin slices for garnish.
Whisk together sugar, flour, baking soda, salt, and cinnamon in a medium bowl. Add diced apple and walnuts, if using; toss to coat.Whisk together eggs, buttermilk, and butter in a small bowl. Gently fold buttermilk mixture into flour mixture until just combined; do not overmix. Divide batter among muffin cups, filling each about three-quarters full. Top each with an apple slice. Bake until muffins are brown around edges and spring back when touched, 16 to 18 minutes. Let muffins cool slightly, about 5 minutes, before turning out of tin onto a wire rack. Serve warm or at room temperature.
Muffins can be stored in an airtight container at room temperature up to 2 days.