Whisk the Manchego, mayonnaise, sour cream, lemon juice, garlic, 1/2 teaspoon salt and a few grinds of pepper in a large bowl.
Heat the oil in a medium skillet over medium-high heat until it shimmers. Add the shrimp, paprika, 1/4 teaspoon salt and a few grinds of pepper and cook, stirring occasionally, until just cooked through, about 3 minutes. Transfer to a plate and cool.
Add the pasta to the boiling water and cook according to the package directions. Drain and rinse under cold water to cool; add to the bowl with the dressing.
Add the shrimp, chickpeas, parsley and red peppers to the bowl and toss to combine. Season with salt and pepper. The pasta salad is best if served right away.
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