Preheat your oven to 375°F (190°C). In a mixing bowl, combine peach slices, strawberries, granulated sugar, and lemon juice. Toss gently until fruit is evenly coated and set aside to let the juices meld.
Pour the fruit mixture into a baking dish, spreading it out into an even layer. The filling should be juicy and fragrant with a hint of citrus.
In a separate bowl, combine flour, rolled oats (if using), brown sugar, and ground cinnamon. Mix well to distribute all dry ingredients evenly.
Add the cold, cubed butter to the dry ingredients. Use your fingers or a pastry cutter to work the butter into the mix until it resembles coarse crumbs with some pea-sized pieces.
Sprinkle the crumble topping evenly over the fruit filling, covering all the fruit for a crispy crust. Gently press it down with the back of a spoon.
Place the baking dish in the oven and bake for about 30 minutes, or until the topping is golden brown and the filling is bubbling around the edges.
Once baked, remove the cobbler from the oven and let it cool slightly for 5 minutes. The aroma will be sweet and inviting, with a warm, fruity scent filling your kitchen.
Serve the cobbler warm, spooned into bowls, perhaps with a scoop of vanilla ice cream or a dollop of whipped cream for extra indulgence.