Preheat your oven to 375°F (190°C) and lightly grease a baking dish.
Peel and slice the peaches into thin, even pieces, then place them in a mixing bowl.
Add finely grated fresh ginger, sugar, and lemon juice to the peaches, then gently toss everything together until the fruit is coated and fragrant.
Pour the coated peaches into your prepared baking dish, spreading them out evenly.
In a separate mixing bowl, combine rolled oats, flour, brown sugar, and cold, cubed butter.
Use your fingers or a pastry cutter to rub the butter into the dry ingredients until the mixture resembles coarse crumbs.
Sprinkle the crumble evenly over the peaches, covering the fruit completely with a golden, textured layer.
Bake in the preheated oven for about 40 minutes, or until the topping is crisp and golden, and the peach filling is bubbling around the edges.
Remove from the oven and let sit for a few minutes so the filling can thicken slightly.
Serve warm, optionally with a scoop of vanilla ice cream or a dollop of whipped cream for extra indulgence.