How to Make It
Preheat oven to 350°F. Coat a 9-inch springform pan with baking spray.
Peel 2 of the apples. Using largest holes of a box grater, coarsely grate peeled apples over a medium bowl. (You should have 2 cups grated apples.) Stir in dried apple and 1 tablespoon honey; set aside.
Stir together flour, sugar, pistachios, ground rose petals, baking powder, 1/2 teaspoon salt, and baking soda in a large bowl until well combined. Make a well in center of dry ingredients. Whisk in eggs, 1/2 cup oil, and grated apple mixture until a thick batter forms.
Spoon batter into prepared pan, smoothing top with an offset spatula. Core and halve remaining apple (do not peel). Thinly slice into half-moons. Starting around border of pan and working your way in, arrange apple slices so they overlap slightly, like petals on a flower, until you reach the middle. When you get to the middle, take the last apple slice and gently roll it into a loose spiral; insert in center.
Bake in preheated oven until a wooden pick inserted in center comes out clean, about 50 minutes. Let cool in pan on a wire rack 10 minutes. Remove sides of pan.
Meanwhile, whisk together lemon juice, rosewater, remaining 2 tablespoons honey, remaining 1 1/2 teaspoons olive oil, and a pinch of salt in a small saucepan. Cook over medium until slightly reduced, about 2 minutes. Remove from heat, and let cool.
Brush top of warm cake with syrup, and let cool completely, about 1 hour.