Cook the pasta according to the package directions.
In a large saucepan, over medium-low heat, warm the cream, milk, 1 1/4 teaspoons salt, and 1/2 teaspoon pepper. Add the cooked pasta and Parmesan and stir until the cheese melts and the sauce thickens, 2 to 3 minutes.
Stir the peas into the pasta until heated through, about 2 minutes. Divide among bowls and top with chives.