Step 1Heat the oven to 350 degrees. Grease a 9-inch cake or springform pan with butter and dust with flour, tapping out the excess.
Step 2In a medium bowl, whisk together the flour, baking powder, salt, ginger and turmeric. In a large bowl, combine the butter and 2/3 cup sugar and beat on medium-low speed of a mixer until smooth, about 1 minute. Add the eggs one at a time, beating to incorporate each fully before adding the next, then beat in the vanilla. Add the dry ingredients and stir with a rubber spatula until the batter just comes together.
Step 3Spread the batter in an even layer in the prepared pan. In a medium bowl, toss the persimmon wedges with the lemon juice until completely coated. Starting from the outside, arrange the persimmon wedges skin side up in a circle at the edge of the batter then work your way toward the center (you may have one or two wedges left over). If there is any lemon juice left in the bowl, pour it over the fruit. Sprinkle the remaining 1 tablespoon sugar evenly over the top of the batter and fruit.
Step 4Bake until a toothpick inserted in the center of the cake (trying to avoid touching the fruit) comes out clean, 40 to 45 minutes. Transfer the pan to a rack and let cool completely before unmolding.