Peel and quarter the potatoes and turnips or swedes.
Place the haggis in a large pan of boiling water and cook according to the packet instructions.
Cook the turnips or swedes and the potatoes in separate pans of boiling salted water for 20 to 25 minutes, or until tender. Drain the veg separately.
Return the turnips or swedes to the pan, add half the butter and mash, keeping chunky. Season to taste. Cover to keep warm.
Trim and roughly chop the spring onions. Melt the remaining butter in the potato pan, add the spring onions and cook for 1 to 2 minutes, or until softened. Add the potatoes and mash until quite smooth, seasoning to taste. Cover to keep warm.
Remove the cooked haggis, cut open and place a portion onto each warmed plate. Divide up the turnips or swedes and potatoes (neeps & tatties) and serve.