In a bowl, combine two-thirds of the minced garlic cloves with the pork rinds and 1 tablespoon of the olive oil and mash to combine.
In a large saucepan, heat 1 inch of vegetable oil to 350°. Add the plantains and fry, keeping the oil at about 300°, until very tender, but not browned, 15 minutes. Drain and transfer the plantains to a large bowl. Using a potato masher, mash the plantains to a coarse puree with 1 tablespoon of the olive oil. Add the garlic–pork rind mixture and mash until evenly combined. Season the mofongo with salt and pepper; keep warm.
In a large skillet, heat the remaining 1/4 cup plus 2 tablespoons of olive oil until shimmering. Add the shrimp and remaining garlic, season with salt and pepper and cook over high heat, stirring occasionally, until curled, about 2 minutes. Add the wine and boil until nearly evaporated and the shrimp are cooked through, about 2 minutes longer.
Spoon the mofongo into bowls and top with the shrimp. Serve right away.