Remove the zest from 2 oranges in strips with a vegetable peeler and finely grate 1 teaspoon zest from the third orange; juice all 3 oranges. Combine the sugar and strips of zest in a skillet and cook over medium heat, undisturbed, until the sugar melts. Swirl the pan and continue cooking, swirling, until dark amber, about 4 minutes. Immediately stir in the orange juice and cook at a rapid simmer until reduced by half, about 15 minutes. Add 1/2 cup cream; simmer until incorporated, about 5 minutes. Remove from the heat; stir in the vanilla. Remove the strips of zest with a slotted spoon and set aside for topping. Let the caramel sauce cool to room temperature, about 45 minutes.
Transfer about two-thirds of the cooled caramel sauce to a medium bowl. In a separate bowl, beat the remaining 2 1/2 cups cream with a mixer until very soft peaks form (do not overbeat). Stir the grated orange zest and 1 cup of the whipped cream into the bowl with the caramel sauce, then fold in the remaining whipped cream.
Line an 8-inch springform pan with plastic wrap. Lay 6 cookies in the pan. Spread 1/2 cup caramel whipped cream on top, then drizzle with 2 teaspoons of the reserved caramel sauce. Repeat to make about 7 more layers of cookies, caramel whipped cream and caramel sauce, ending with a layer of caramel whipped cream.
Cover the cake with plastic wrap; chill at least 6 hours or overnight. Uncover, invert onto a plate and remove the pan and plastic wrap. Top with the candied orange zest.