Preheat oven to 375F (190C). Also, set a large pot of salted water to boil.
Trim asparagus spears to fit into a rectangular tart pan (with removable bottom). Toss trimmed asparagus into boiling salted water for about 2 minutes to blanch.
Boil potatoes for 12 minutes in salted water. Drain.
While potatoes are boiling, layer phyllo into tart pan, leaving about 1" of dough overhanging the edge of the pan. Butter each sheet as it goes into the pan.
Mash potatoes with Cheddar and Lancashire cheeses. Add salt and pepper to taste. Add nutmeg and cream. Add eggs and mix well. Pour into tart pan. Lay asparagus spears on top, alternating directions of tips. Brush top lightly with any remaining melted butter. Crimp overhanging phyllo up along edge of tart pan. Put pan on the lowest shelf of the oven for 15-20 minutes. Remove pan from oven and allow it to set for at least 15 minutes.