Heat oven to 375F. Lightly butter a 2-quart baking dish.
In a large bowl, toss peaches with sugar, cornstarch, lemon juice, vanilla, and salt.
Meanwhile, whisk flour, oats, brown sugar, cinnamon, and salt. Work in butter with your fingers until you have damp, pea-sized clumps. Everything should be evenly moistened, no dry flour.
Spread peaches in the dish. Scatter topping evenly over the top, breaking apart the large clumps.
Bake 40 to 45 minutes, until the filling bubbles at the edges and the topping is deep golden. Cover loosely with foil after about 25 minutes, or whenever the topping is getting quite brown. Rest 10 minutes before serving so the filling sets.
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Notes
Baking dish: A 2-quart dish is an 8x8 inch square, an 11 by 7 inch rectangle, or an 8 to 9 inch round, about 2 inches deep.Frozen peaches: Use straight from the freezer and add about 10 minutes to the bake time.Storage: Cover loosely and keep at room temperature 1 day or refrigerate up to 4 days. Reheat at 350F for 15 minutes.