1. To make gremolata: Combine chopped parsley, lemon zest, and diced garlic in a small bowl; set aside.
2. Cook pasta in a large saucepan according to package directions. When 3 minutes of cooking time remains, add the asparagus; finish cooking. Drain in a colander; rinse with cold water.
3. Heat the same saucepan over medium heat; add cream, 1/2 teaspoon salt, and 1/8 teaspoon pepper. Add pasta mixture to pan; toss to coat. Increase heat to medium-high; bring cream to a boil. Cook until almost all of the cream is absorbed (about 3 minutes), stirring constantly. Add half of gremolata to pan; cook 1 minute, stirring constantly.
4. Transfer to serving bowls; top with remaining gremolata. Serve immediately.