Make the crust: With a rack in the center position, preheat the oven to 350°F.
Stir the crushed cookies, pecans, sugar, cinnamon, and salt together in a mixing bowl. Stir in the melted butter until the crumbs are evenly moistened. Press the crust mixture into an even layer over the bottom of a 9--inch springform pan. Bake until the crust is lightly browned and firm, about 15 minutes. Let cool completely.
Make the filling: While the crust cooks, cut a 6--inch square from a double thickness of cheesecloth. Crumble the cinnamon sticks onto the square, add the vanilla beans, and tie the cheesecloth into a neat bundle. Put the cream, milk, and rice in a large saucepan. Drop in the spice bundle and heat, stirring, to a simmer. Add the salt and simmer, stirring occasionally, until the rice is tender, about 15 minutes.
While the rice is cooking, soften the gelatin: Pour the water into a small bowl. Sprinkle the gelatin over the surface, slowly and evenly to prevent lumps from forming. Whisk with a small fork until the gelatin is softened and the mixture is fluffy.
Stir the sugar into the cooked rice and remove from the heat. Stir in the cream cheese until the cheese is melted and the sugar is dissolved. Pour half the rice mixture into a sieve set over a bowl and, using a wooden spoon, mash the rice against the sieve to squeeze as much of the liquid from it as possible. Some rice will pass through the sieve too; that is fine. Scrape the mashed rice from the bottom of thesieve into the bowl with the liquid. Transfer the rice in the sieve to another bowl, and repeat with the remaining rice mixture. Measure out 2 cups of the reserved rice and stir into the liquid; discard the remaining rice. Whisk about 1 cup of the rice mixture into the softened gelatin until the gelatin is dissolved, then stir back into the rice mixture until thoroughly blended.
Pour the rice mixture over the cooled crust. Refrigerate the cake until completely chilled and set, at least 4 hours, or up to 1 day.
To serve, release the sides of the springform pan—run a knife dipped in warm water between the cake and the sides of the pan to free the cake completely. Cut the cake into wedges, making sure to cut all the way through the crust, and serve, passing the caramel sauce separately.
Note: Maria cookies are crisp round cookies with a pleasant, simple flavor, not unlike animal crackers—which make a good substitute. Maria cookies can be found in many Latin groceries and online at www.tienda.com.