Preheat your oven to 375°F (190°C). Lightly grease an 8x8 or 9x9 inch baking dish.

Prepare the peach filling: In a large bowl, combine the sliced peaches, granulated sugar, 2 tablespoons of flour, lemon juice, cinnamon, and nutmeg. Toss gently to coat the peaches evenly. Pour the mixture into the prepared baking dish and spread into an even layer.

Make the crisp topping: In a separate medium bowl, whisk together 1 cup of flour, brown sugar, rolled oats, and salt.

Add the cold, cubed butter to the dry ingredients. Use a pastry blender, your fingertips, or a fork to cut the butter into the mixture until it resembles coarse crumbs with some pea-sized pieces of butter remaining.

Evenly sprinkle the crisp topping over the peach filling in the baking dish.

Bake for 35-45 minutes, or until the topping is golden brown and the peach filling is bubbly and tender. If the topping starts to brown too quickly, you can loosely tent the dish with aluminum foil.

Let the peach crisp cool for at least 10-15 minutes before serving. This allows the filling to thicken slightly. Serve warm, perhaps with a scoop of vanilla ice cream or a dollop of whipped cream.