Prepare the Pecan Streusel: Preheat oven to 350°F. Stir together chopped pecans, brown sugar, cinnamon, salt, 3/4 cup flour, 1/2 cup granulated sugar, and 1 teaspoon ground cardamom in a medium bowl. Add 1/2 cup cold butter pieces, and, using your fingers or a pastry blender, combine until a sandy texture is achieved.

Prepare the Cake: Sift together baking powder, 1 1/2 cups flour, 3/4 cup granulated sugar, and 1/2 teaspoon cardamom. Beat cream, vanilla, egg, and 4 tablespoons melted butter with an electric mixer on medium-high speed until frothy, about 1 minute. Fold in the flour mixture with a spatula until blended. Do not overmix.

Gently rub peaches under running water to remove fuzz, and slice each into 8 wedges. Transfer the batter to a lightly greased and floured 9-inch springform pan, and smooth the surface. Arrange the peach slices evenly over the batter, pressing them into the batter just a bit. Cover the top evenly with the Pecan Streusel, pressing lightly.

Bake in preheated oven until a toothpick inserted in the center comes out clean, about 1 hour. Cool in pan on a rack 1 hour. Remove sides of pan before serving.