1Preheat oven to 350°F. Grease a high sided 9-inch cake pan with cooking spray and line with parchment. Slice the peaches and arrange them in a pan in concentric circles.
2In a medium saucepan, combine ¾ cup of the sugar with 2 tablespoons of water over medium-high heat. Cook, shaking the pan if needed, until an amber caramel forms, about 6 minutes. Immediately pour over the peach slices in an even layer.
3In a large bowl, whisk the remaining 1 cup granulated sugar, the brown sugar, oil, butter, and eggs until smooth. Add the buttermilk and whisk until incorporated, followed by the vanilla and almond extract.
4Add the flour, salt, baking soda, and baking powder to the bowl and fold until just incorporated, then pour over the caramel-coated peaches. Bake until the top is golden and a toothpick inserted into the centre comes out clean, about 1 hour.
5Let cool 15 minutes, then run a paring knife along the edges of the cake. Place a plate over the cake pan and invert, discarding parchment paper. Let cool slightly, then slice and serve warm.