Scoop avocado flesh into the bowl of a food processor. Add lime juice, and season with salt; process until smooth. Transfer to a small bowl; set aside.
Preheat oven to 300 degrees. Arrange bread slices on a baking sheet, and bake, turning once, until dried out and slightly toasted, 10 to 14 minutes. Let cool on a wire rack.
Heat a large skillet over medium heat. Add oil and achiote paste, and cook, stirring, 1 minute. Add shrimp; cook, stirring occasionally, until shrimp are pink and cooked through, about 4 minutes. Transfer to a bowl, and let shrimp cool slightly.
Using a small offset spatula, spread 1 tablespoon avocado puree on each bread slice. Using an 1 1/2-inch round cookie cutter, cut out 4 rounds from each slice. Top each round with a shrimp; top shrimp with sour cream and fish roe. Garnish with cilantro.
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