To make the black bean cakes, combine first 6 ingredients in a food processor, pulse until chunky. Add salt to taste, then add egg and pulse again to combine. Shape mixture into 8 cakes. If you have time, place cakes in the fridge for an hour or more to firm up.
To make salsa, cook corn on a grill pan or BBQ over high heat until nicely charred, turning every so often to distribute the heat evenly. Let corn cool and use a sharp knife to remove kernels. In large bowl, combine corn kernels with next eight ingredients and season with salt to taste.
When ready to cook cakes, preheat oven to 350 degrees.
In large sauté pan, heat 2 tablespoons olive oil over medium high. Add as many black bean cakes as will fit comfortably (we fit four at a time) and cook for three minutes on each side. As cakes cook, remove to baking sheet; when all cakes have been fried, bake in oven for 10 minutes.
While black bean cakes are in the oven, fry up tortilla crisps. Wipe out the sauté pan with a paper towel, add three tablespoons olive oil, and turn heat to medium high. Add sliced tortilla strips and a generous pinch of salt, and cook until crispy (about five minutes), shaking the pan frequently to make sure they cook evenly.
To serve, place two black bean cakes on each plate, top with charred corn salsa, and garnish with tortilla strips. Serve with fresh lime wedges on the side.