In a large mixing bowl, whisk together the eggs, dulce de leche, cinnamon, cardamom, allspice, and salt until well combined. Add the evaporated milk, cream, and vanilla and stir until well combined, being careful to not whisk too vigorously to limit air bubbles forming.
5 When the caramel in the cake pan is set, pour the custard through a fine mesh sieve into the cake pan. Discard any lumps of dulce de leche or spices caught in the sieve.
6 Place the roasting pan with the cake pan inside it in the oven. Fill the roasting pan with 1-inch of hot water.
7 Bake for 50 minutes or until the edges are set and the center wobbles when gently shaken. Remove from the oven and let the custard cool to room temperature in the water bath. Remove from the water bath and chill for at least 3 hours or up to 24 hours.
8 When ready to serve, dip the bottom of the pan in hot water for several seconds. Run a knife around the edge of the custard to loosen it. (It should shimmy in the pan if shaken. If not, dip in the water for a few seconds more.) Place a large, rimmed plate on top of the cake pan. Quickly flip the plate and pan to invert the custard. Remove the pan. Serve cold or at room temperature. Store the flan covered and refrigerated for up to 3 days.