In a large pot, heat ¼ cup olive oil. When almost smoking, add onion, carrot and 1 clove smashed garlic and sauté until vegetables are soft, about 5 minutes. Add the canned tomatoes with juice, clam juice and white wine. Bring to a boil and simmer on medium heat for 10 minutes, uncovered. Remove from heat and allow to cool slightly. Carefully pour tomato mixture in the bowl of a food processor and puree. Add a couple of tablespoons of water if needed – you want to end up with a broth. Check for seasoning.
Return broth to the pot. Add 1 cup of water and 2 tablespoons extra virgin olive oil and bring to a boil. Reduce heat and add 2 cups Fregola Sarda. Cover pot and simmer until done. Fluff with a fork and season with salt and pepper.
In a large skillet, add the remaining ¼ cup oil and the 2 cloves of minced garlic. Heat the oil, making sure not to burn the garlic. When the oil is hot, add the shrimp and stirring occasionally, cook the shrimp until they start to turn pink, about 5 minutes. Be careful not to overcook the shrimp or they will become tough. Remove from heat and add the lemon juice, red pepper and chopped parsley. Check for seasoning.
To serve, place the Fregola Sarda in the center of a platter and top with the shrimp.