In a medium, deep pan over medium-high heat, heat the oil until hot, but not smoking, or when it reaches a temperature between 360°F and 375°F on a deep-fat thermometer. You can test the oil for readiness by dropping in a piece of zucchini and if it sizzles immediately it is ready. Working in batches, fry the zucchini until golden brown, about 2 to 3 minutes. Do not overcrowd the pan. Using a wire skimmer, transfer the zucchini to a paper towel lined plate to drain thoroughly.
Bring a large pot of water to a rolling boil. Salt the water and drop in the pasta. Stir to separate the strands and cook until the pasta is just under al dente, tender but firm to the bite, stirring occasionally with a wooden spoon. Drain the pasta in a colander, reserving 1 1/2 cups of the pasta cooking water.
Meanwhile, in a large skillet over moderate heat, combine the olive oil and garlic and stir until barely fragrant, about 15 to 20 seconds. Add the shrimp and stir for 30 seconds. Add the zucchini and one-half of the blossoms and stir briefly, about 30 seconds longer. Season with salt and a generous pinch of pepper. Pour in 1 cup of the pasta cooking water and the cream and stir to combine thoroughly.
Add the pasta, Parmigiano, and basil to the pan and toss until the pasta is well coated with the sauce, about 2 minutes, adding a little more pasta cooking water, if more liquid is needed. Towards the end of the cooking, sprinkle in the remaining zucchini blossoms and toss again to combine. Taste for seasoning and add more salt and pepper, if necessary.
Divide the pasta among the plates and serve immediately garnished with the reserved zucchini blossoms and basil.