In a bowl, whisk the crème fraîche with the buttermilk, mint, chives, lemon zest and 1 minced garlic clove; season the crema with salt and pepper.
In a blender, combine the remaining minced garlic with the chiles, cardamom, cumin and lemon juice. Puree until smooth. Season the cardamom sauce with salt and pepper.
Put the beaten egg and panko in separate bowls. Dip the shrimp in the egg, then dredge in the panko; transfer to a baking sheet. Refrigerate for 10 minutes.
Preheat the oven to 350°. In a saucepan, heat 1 inch of vegetable oil to 350°. Fry 4 shrimp at a time, turning once, until browned and crisp, about 2 minutes. Transfer the shrimp to a rack set over a rimmed baking sheet to drain; season with salt. When all of the shrimp have been fried, transfer them to the oven and bake until heated through, about 2 minutes.
Spread the warm flatbreads with the spicy sauce. Arrange the avocado and the shrimp on top. Scatter the pickled onion on top, drizzle with the crema and serve.