Preheat oven to 350 degrees F. Butter a 9-inch springform pan and line the bottom with parchment. For the streusel, combine flour, brown sugar, and cinnamon in a bowl. Work in the cold butter with your fingertips until the mixture holds together in clumps when squeezed. Refrigerate until needed.

Beat softened butter and granulated sugar in a large bowl until light and fluffy, about 3 minutes. Add eggs one at a time, beating well after each. Mix in sour cream and vanilla. In a separate bowl, whisk together flour, baking powder, baking soda, and salt. Add dry ingredients to the butter mixture in two additions, mixing just until no streaks remain.

Spread half the batter into the prepared pan. Arrange half the peach slices in a single layer over the batter, pressing them in slightly. Dollop and spread the remaining batter on top. Arrange the remaining peaches over the surface, then scatter the streusel evenly, breaking it into pea to walnut-sized pieces.

Bake until the top is deep golden and a toothpick inserted into the center comes out clean, 50 to 55 minutes. The streusel should look crisp, not pale. Cool in the pan on a wire rack for 15 minutes, then run a knife around the edge and remove the springform ring. Serve warm or at room temperature.