Rinse fish and pat dry. Cut into chunks and place in food processor .
In a cup, combine the coconut milk, fish sauce, shrimp paste, chili powder, cumin, ground coriander, and brown sugar. Stir with a fork to combine, then pour into the processor over the fish.
Add remaining ingredients (kaffir lime leaf strips, green onion, galangal/ginger, garlic, and chili). Pulse to create a thick fish paste.
Picking up a small amount in your hand (about the size of a golf ball) pat the paste into a small cake and set on a clean plate. Note that traditional Thai fish cakes are small (about 2 inches in diameter and 3/4 to 1 inch thick) and not too thick. If your paste is too wet to easily form into cakes, add a little flour or breadcrumbs to the mix. As you continue making the cakes, it helps to rinse your hands every so often with cool water to prevent paste from sticking.
Set plate of cakes in the refrigerator for 10 minutes to firm up. Meanwhile, prepare your pan for frying as well as your garnishes.
Dice cucumber into small cubes.
Pour oil into a small frying pan or wok (at least 1 inch deep).
Heat oil. When hot enough (a breakcrumb should sizzle and cook immediately when dropped in), gently place cakes in oil. Allow to fry 30 seconds to 1 minute before turning, gently lifting cakes from the bottom of the pan (they may stick a little). Fry until golden-brown and drain on paper towel.
Serve fish cakes immediately with the chopped cucumber and Thai sweet chili sauce drizzled over. Top with fresh cilantro and a squeeze of lime juice just before eating.