Place butter in a medium saucepan and warm over medium-low heat. The butter will melt, then foam and bubble, then start to brown. You will notice little brown bits forming at the bottom of the pan. Stir frequently during this process and keep your attention on the pot. The butter can go from wonderfully brown to burnt in just a few moments. You will know the butter is done when it gives off a nutty aroma and turns a golden brown. Set aside and let cool.
Preheat your oven to 350°F. Line the bottom of a 10-inch cast iron skillet with parchment paper (or you could use a springform pan). Grease both the parchment and the sides of the skillet generously with butter, and set aside.
In a medium bowl, whisk flour, baking powder, salt and allspice until combined. In a large bowl, whisk together 1/2 cup cooled browned butter and sugar. Reserve remaining 1/4 cup brown butter for the topping. One at a time, whisk in eggs, then stir in buttermilk. Add the flour mixture into the browned butter-egg mixture, and stir until just combined. Pour the batter into the prepared skillet. Toss peach wedges with lemon juice, and arrange them in a single layer on top of the batter.
To prepare the streusel topping, combine remaining 1/4 cup brown butter, brown sugar, flour, pecans, cinnamon and sea salt in a small bowl. Mix until large crumbs form (I used my hands here). Sprinkle the topping evenly over the peaches.
Transfer the skillet to the oven, and bake until the top is golden brown, and an inserted toothpick comes out with moist crumbs (40 to 45 minutes). Let cool for 5 minutes on a rack before serving.