Preparation:
1. In the bowl of the food processor (or you can use a blender), add the rice cakes and pulse until you get 1 1/4 cups rice cake crumbs. Return 1/4 cup crumbs to the food processor, reserving the remaining 1 cup for coating the cakes.
2. Add shrimp, shallot, 4 tablespoons each of the cilantro and basil, and 2 tablespoons jalapeño to the crumbs. Add 2 teaspoons fish sauce and a pinch each salt and pepper. Pulse until the mixture forms a coarse, chunky paste. (Be careful not to overprocess; if using a blender, scrape down the sides frequently.) Transfer to a bowl, cover and refrigerate while you make the sauce (at least 15 minutes and up to 24 hours).
3. In a small bowl, whisk together mayonnaise, remaining cilantro, basil, jalapeño and fish sauce. Zest the lime into the bowl, then cut the naked lime into wedges and squeeze in some juice. Salt to taste. Reserve extra lime wedges for serving.
4. Spread remaining 1 cup rice cake crumbs out onto a plate or sheet pan. With wet hands to keep shrimp paste from sticking, form 2 tablespoons of shrimp mixture into a 1/2-inch-thick patty and put it on top of the crumbs. Repeat with remaining shrimp mixture, re-wetting your hands as necessary. Turn the patties over in the crumbs to coat both sides.
5. Heat oil in a large skillet over medium-high. Fry patties in batches until golden brown, 3 to 4 minutes per side. Serve shrimp cakes topped with more basil leaves, with chile-lime sauce for dunking and lime wedges on the side for squeezing.
And to drink …
The combination of herbs, pungent fish sauce and chile heat, along with the mild shrimp flavor of these cakes, would put me in the mood for aromatic, herbal whites with racy acidity and minimal oak flavoring. Austrian grüner veltliners, German rieslings (dry or sweet), restrained sauvignon blancs — all of these would be terrific with this dish, just as they would be with many Southeast Asian preparations.