Add nuts, oats, brown sugar, cinnamon, and salt; toss to coat in butter.
Cook, stirring frequently, until golden and lightly browned, about 5-8 minutes.
Remove to a plate. The topping will crisp up as it cools.
Add 1 tablespoon butter to the now-empty skillet.
Stir in the peach slices and granulated sugar.
Cook until the peaches are soft, about 5-6 minutes.
To serve, divide peaches between bowls and sprinkle with topping.
Notes
Peaches should be thinly sliced (about 1/4-inch thick). Slicing the peaches thicker will make it take longer for them to cook. See the notes above the recipe about peeling peaches.