Remove sardines from tin, reserving oil, and place fish in a mixing bowl. Add remaining fish cake ingredients, along with the oil from one tin (about 2 TB) to the bowl.
Gently mix all the ingredients together with a fork. Mix until incorporated, and then stop. (Do not use a blender or food processor for this step, because you don't want to purée the fish.)
Use a 1 TB measuring spoon (or another small scoop) and scoop the fish cake mix into small balls.
One by one, roll the balls in your hands, and then flatten into small patties 2" across, and about 1/2" thick. You should end up with 15 - 18 patties, depending on the size of your scoop.
Set patties on a rimmed baking sheet, large cast iron pan, or casserole dish. (Note: We've added oil to an oily fish. While cooking, oil from the fish will drain out of the fish, and the fish will fry in the oil under the broiler. Avoid using a rimless baking sheet, because the oil will drip all over your oven.)
Refrigerate patties for about 30 minutes.
While fish cakes chill, mix together all the ingredients for the yogurt sauce. Make sure to taste as you add the cayenne and salt-- use more or less as desired. Put sauce in the refrigerator until it's time to serve.
Move oven rack to the top 3rd of the oven (or about 6" from the broiler). Broil 5 minutes, flip, and broil 3-5 minutes more, until fish cakes are dark and golden.
Remove cakes from pan (and residual oil) immediately. Serve while still hot with the yogurt sauce.
Leftovers:Store leftover patties in the fridge, and use within 1-2 days. Use the sauce within a week.
Make Ahead + Freeze: Let sardine cakes cool, and then wrap individually and tightly with wax paper, plastic wrap, or foil. Store in an air-tight container in the freezer, and use within three months. To reheat, simply unwrap and cook again. Cook until golden. Patties may take 2-3 minutes longer to cook from frozen.Sauce should not be frozen.