Bring a large pot of salted water to a boil. Meanwhile, make the pesto: Process the tomatoes, basil, mint, almonds, garlic, orange zest and 1 teaspoon salt in a food processor until combined. With the motor running, gradually add 1/3 cup olive oil in a steady stream and blend to make a coarse pesto, scraping down the sides of the processor as needed. Transfer the pesto to a large bowl; do not wash out the processor.
Add the bucatini to the boiling water and cook as the label directs. Meanwhile, heat about 1/4 inch of olive oil in a large skillet over medium-high heat. Put the flour in a shallow dish. Season the shrimp with 1/2 teaspoon salt, then dredge in the flour. Fry the shrimp in 2 batches until golden and crisp, about 2 minutes per side. Drain on paper towels and sprinkle with salt.
Remove the pasta with tongs (reserve the cooking water) and transfer to the bowl with the pesto; toss to coat. If the pasta seems dry, rinse the food processor with 1/2 cup of the reserved cooking water and add to the pasta, a little at a time. Season with salt. Add the cheese and toss. Drizzle the pasta with olive oil and divide among bowls; top with the shrimp.
Photograph by Anna Williams
Recipe courtesy Food Network Magazine