Cover the rutabaga and potatoes with cold, generously salted water in a large pot and bring to a boil over medium-high heat. Reduce the heat and simmer until the vegetables are fork-tender, about 30 minutes.
Drain the vegetables and return to the pot over low heat. Stir in 8 tablespoons butter. Mash with a potato masher, ricer or food mill until smooth, adding the warm half-and-half and 2 teaspoons salt. Keep warm while preparing breadcrumbs.
Melt the remaining 4 tablespoons butter with the olive oil in a large skillet over medium-high heat. Add the lemon zest and scallions. Add 1/2 teaspoon salt and cook, stirring, until fragrant, about 2 minutes. Add the parsley and breadcrumbs and cook over medium-low heat, stirring until evenly toasted, 3 to 4 more minutes. (If the breadcrumbs toast too quickly, reduce the heat.)
Transfer the mashed vegetables to a large shallow platter and sprinkle with the breadcrumbs just before serving. Garnish with scallion slices. (To curl them, julienne whole scallions and place in ice water.)