Preheat oven to 350°.
Cut tops off persimmons; scrape pulp away from skin with a spoon. Place persimmon pulp, milk, sugar, and eggs in a food processor or blender, and process until smooth.
Lightly spoon flour into dry measuring cups; level with a knife. Combine flour and next 4 ingredients (through salt) in a large bowl; make a well in center of flour mixture.
Gradually add persimmon mixture to flour mixture, stirring just until blended. (Batter will be thin but will thicken quickly.) Let batter stand for 10 minutes to thicken. Pour batter into a 9-inch springform pan coated with cooking spray.
While batter stands, melt butter in a small skillet over medium-high heat. Add chopped pecans; cook 3 minutes or until pecans are toasted. Sprinkle pecan mixture over batter. Swirl pecan mixture into batter using a knife or skewer. Bake at 350° for 1 1/2 hours or until cake is set in the center and a skewer inserted into center comes out clean. Let cool 15 minutes; remove cake from pan. Cut into wedges.