Preheat oven to 350°F (175°C). Line an 8x8-inch baking pan with parchment paper.
In a large bowl, combine flour, oats, brown sugar, cinnamon, and salt.
Pour in melted butter and mix until crumbly.
Reserve 1 cup crumb mixture for topping.
Press remaining crumb mixture firmly into prepared baking pan.
Bake crust for 10 minutes.
In another bowl, combine diced peaches, sugar, cornstarch, lemon juice, and vanilla extract. Mix gently.
Spread peach filling evenly over warm crust.
Sprinkle reserved crumb topping over peaches.
Bake for 35–40 minutes until topping is golden brown and filling is bubbly.
Allow bars to cool completely before slicing.
Dust with powdered sugar or drizzle with glaze if desired.