Peel and slice the peaches into 1/2-inch thick wedges, then transfer to a large bowl. Add the brown sugar, sugar, cinnamon, nutmeg, ginger, vanilla, almond extract, salt, lemon juice, and cornstarch to the peaches and toss gently to combine, ensuring the cornstarch is evenly distributed to help thicken the filling as it bakes. Set aside at room temperature—the peaches will release their juices as they sit, which is exactly what you want for a flavorful filling.

In a medium bowl, whisk together the flour, sugar, baking powder, cinnamon, and salt. Cut the cold butter into 1/2-inch cubes and add to the flour mixture. Using a pastry cutter, fork, or your fingertips, work the cold butter into the flour until the mixture resembles coarse breadcrumbs with some pea-sized pieces of butter still visible—this creates a flaky texture. Pour in the buttermilk and vanilla, then gently knead the dough for 2-3 minutes until just combined (don't overwork it or the biscuits will be tough). Wrap the dough and refrigerate for at least 15 minutes while you prepare the streusel.

In a small bowl, combine the flour, brown sugar, cinnamon, and salt. Pour the cooled melted butter over the mixture and stir with a fork until the mixture is evenly moistened and crumbly. The streusel should hold together slightly when pinched but still look loose and chunky. Set aside at room temperature until needed.

Heat your oven to 375°F. Pour the peach filling from Step 1 (including all the accumulated juices) into a 10-12 inch cast iron skillet. Break the chilled biscuit dough from Step 2 into irregular 2-3 inch pieces and scatter them evenly over the peaches, leaving some gaps so steam can escape—this isn't a neat topping, and those gaps are intentional.

Sprinkle the cinnamon streusel from Step 3 evenly over the biscuit pieces and into the gaps between them. I like to use my fingers to crumble the streusel as I sprinkle it for a more rustic, uneven texture that bakes up beautifully crispy. Place the skillet in the preheated oven and bake for 45-50 minutes, until the biscuit topping is golden brown and the peach filling is bubbling around the edges. The cobbler is done when a toothpick inserted into the thickest part of a biscuit comes out clean.

Remove the skillet from the oven and let it cool for 10-15 minutes before serving. This resting time lets the filling set slightly so it won't run all over the plate, while the cobbler is still warm enough to serve with vanilla ice cream or whipped cream. Serve directly from the warm skillet for a rustic presentation.