To prepare topping, place butter in a small saucepan; cook over medium heat 3 minutes or until browned and very toasty-fragrant. Remove from heat; stir in oil and vanilla. Cool slightly.
Weigh or lightly spoon flour into a dry measuring cup; level with a knife. Combine flour, oats, 1/2 cup sugar, and salt in a medium bowl; drizzle with butter mixture. Toss well to completely incorporate so there are no floury bits left.
To prepare filling, place peaches in a large bowl. Combine 1/3 cup sugar and cornstarch, stirring well; sprinkle over peaches. Toss well to combine. Spoon peach mixture into a 2-quart glass or ceramic baking dish coated with cooking spray. Top with topping. Bake at 375°F for 40 minutes or until topping is lightly browned and filling is bubbly. Serve warm.
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