Place potatoes in a medium saucepan; add water to cover by 2 inches, and bring to a boil over medium-high. Reduce heat to medium, and bring to a simmer. Simmer until very tender, 15 to 18 minutes. Drain potatoes, and return to saucepan.

While potatoes cook, cook cauliflower according to package directions; transfer to a colander, and drain, pressing with paper towels to remove excess water. Add drained cauliflower to potatoes in pan. Cook over medium until cauliflower and potatoes are mostly dried out, 2 to 3 minutes, stirring occasionally to allow excess steam to evaporate.

Place half of potato mixture in a blender with half each of sour cream, butter, Parmesan, and salt. Secure lid on blender, and remove center piece to allow steam to escape. Place a clean towel over opening. Process until smooth, about 45 seconds, stopping to scrape down sides as needed. Transfer to a large bowl, and repeat with remaining cauliflower, potatoes, sour cream, butter, Parmesan, and salt. (Or use a food processor.) Sprinkle with black pepper and chives, and serve.