In a small bowl, toss the shallot rings in the flour until coated. In a 10-inch skillet, heat 3 Tbs. of the oil over medium-high heat until shimmering. Working in two batches, cook the shallot rings until golden brown, adding more oil if necessary, 3 to 4 minutes. Using a slotted spoon, transfer to a paper-towel-lined plate and sprinkle lightly with salt.
In a 2-quart saucepan, boil the shrimp shells in 2 cups of well-salted water until the water is reduced to 1-1/2 cups, about 5 minutes. Strain and set aside.
Season the shrimp with 1/2 tsp. salt and 1/2 tsp. pepper. In a 12-inch skillet, heat 2 Tbs. of the oil and the butter over medium-high heat. Add half of the shrimp and cook until just cooked through, about 30 seconds per side. Transfer to a plate and repeat with the remaining shrimp.
Add the remaining 2 Tbs. oil, the garlic, and shallot strips to the skillet and cook, stirring, until golden brown in spots, 2 to 3 minutes. Add the Madeira and cook until almost fully evaporated, about 3 minutes. Add the tomatoes and cook until most have burst and their liquid is reduced by half, 4 to 5 minutes. Add the cream and 1/2 cup of the shrimp broth; cook until the sauce thickens, 4 to 5 minutes. Add the shrimp and cook until just heated through. Season to taste with salt and pepper.
Meanwhile, bring a 6-quart pot of well-salted water to a boil. Cook the pasta according to package directions until al dente. Drain the pasta. Add the pasta and capers to the sauce and toss, adding some of the remaining shrimp broth to loosen the sauce, if necessary. Divide the pasta among four shallow bowls, garnish with the chives and fried shallots, and serve.
nutrition information (per serving):
970, Fat Calories
51, Saturated Fat
5, Polyunsaturated Fat
18, Monounsaturated Fat
Photo: Scott Phillips