Bring a large pot of salted water to a boil and cook the chickpea pasta according to package directions until al dente.
While the pasta boils, dice the chicken breast into bite-sized pieces and season with the sea salt and black pepper.
Heat the olive oil in a large skillet over medium heat and sauté the chicken until golden brown and cooked through, approximately 6 to 8 minutes.
In a high-speed blender, combine the drained roasted red peppers, Greek yogurt, garlic clove, nutritional yeast, and smoked paprika; blend until completely smooth.
Drain the cooked pasta, reserving 2 tablespoons of the starchy pasta water.
Reduce the skillet heat to low and pour the red pepper sauce into the pan with the chicken, adding the reserved pasta water to thin the sauce if needed.
Add the cooked pasta to the skillet and toss gently until every noodle is evenly coated and the sauce is warmed through.
Serve immediately garnished with freshly chopped basil for a bright, herbaceous finish.