Bring a large sauce pot of lightly salted water to a boil for the rumbledethumps.

• Peel, core, and coarsely chop the apple.
• Trim the root end from the rutabaga; peel and coarsely chop the rutabaga. Set aside all but ½ cup [1 cup] rutabaga for the rumbledethumps.

In a small sauce pot over medium-high heat, warm 1 teaspoon oil until hot but not smoking. Add the apple and ½ cup [1 cup] rutabaga and cook, stirring occasionally, until the apple is softened and the rutabaga is lightly browned, 3 to 5 minutes.
Add the chutney base and ½ cup [1 cup] water and bring to a boil. Reduce to a simmer and cook, stirring occasionally, until the rutabaga is tender, 8 to 10 minutes. Remove from the heat and season to taste with salt and pepper.
While the chutney cooks, prepare the rumbledethumps.

• Peel the turnip and coarsely chop.
• Strip the parsley leaves from the stems; coarsely chop the leaves. Set aside half for garnish.

To the pot of boiling water, add the turnip and remaining rutabaga and cook, stirring occasionally, until tender, 10 to 12 minutes. Stir in the cabbage and cook until tender, 1 to 2 minutes.
Drain the vegetables and return to the pot. Using a fork, masher, or the bottom of a bowl, mash the vegetables. Stir in half the parsley and season to taste with salt and pepper.
While the rumbledethumps cooks, prepare the pork.

• Pat the pork dry with a paper towel; season with salt and pepper.

In a large frying pan over medium-high heat, warm 1 to 2 tablespoons oil until hot but not smoking. Add the pork and cook, turning frequently, until browned but still faintly pink within, 8 to 10 minutes. Transfer to a plate.

Transfer the pork to individual plates, top with the apple chutney, and garnish with the remaining parsley. Serve the rumbledethumps on the side.