Cook butter in a small skillet over medium heat, stirring often, until it foams, then browns, 5–7 minutes. Pour brown butter into a 13x9" baking dish. Whisk flour, baking powder, salt, and remaining 1¾ cups sugar in a medium bowl. Whisk in milk and vanilla, then pour batter into baking dish by the ladleful so butter swirls and mixes into batter. Top with peaches.
