Toast rice in a small skillet over medium, stirring often, until golden brown, about 8 minutes; process toasted rice in a coffee grinder until it reaches a sand-like texture.
Heat 2 tablespoons canola oil in skillet over medium-high; cook shallots and garlic in hot oil, stirring often, until golden brown, about 3 to 4 minutes. Using a slotted spoon, transfer shallot mixture to a plate lined with paper towels.
Stir together lime juice, fish sauce, and gochugaru in a large bowl.
Pour canola oil to a depth of 3 to 4 inches into a Dutch oven; heat to 360°F. Whisk together tapioca flour and white rice flour; dredge shrimp in flour mixture. Fry shrimp in hot oil, in 2 batches, until golden and crispy, about 4 minutes per batch. Drain on paper towels.
Transfer shrimp to lime juice mixture; add shallot mixture, ground toasted rice, scallions, cilantro, and mint, and toss until well combined.
Place each cabbage leaf on a small plate. Mound 1/2 cup shrimp mixture on each cabbage leaf, and surround each with 2 to 3 cucumber slices.