Cut each peach in half, then cut each half into 4 slices.
Melt the butter in a large skillet over medium heat. Reduce heat to medium-low, sprinkle the sugar over the butter, and stir until dissolved, about 1 minute. Add the peaches, increase heat to medium-high, and cook, stirring frequently, until the peaches are softened and coated with a thin sauce, about 3 minutes. Remove from heat and let stand a few minutes.
Meanwhile, in a bowl, beat the cream and vanilla until soft peaks form. Spoon the peaches and sauce into bowls and serve with a dollop of whipped cream.