Blend flour and salt in processor.
Add butter and cut in, using on/off turns, until coarse meal forms.
Add 4 tablespoons ice water.
Using on/off turns, blend until moist clumps form, adding more water by 1/2 tablespoonfuls if dough is dry.
Gather dough into a ball.
Flatten into disk, wrap in plastic and chill for at least 1 hour and up to 1 day.
Mix 2 tablespoons butter and flour in bowl to a smooth paste; set aside.
Melt 2 tablespoons butter with oil in large deep skillet.
Add mushrooms, shallots and thyme.
Saute until mushrooms brown, about 8 minutes.
Add sausage and saute until no longer pink, about 7 minutes, breaking up as you go.
Sprinkle with salt and pepper to taste.
Saute until chicken is no longer pink on outside, about 5 minutes.
Add Madeira and boil 2 minutes.
Add broth and bring to boil.
Mix in butter/flour paste.
Simmer until sauce thickens, stirring often, about 3 minutes.
Mix in parsley.
Season with salt and pepper.
Transfer to 10-cup round baking dish.
Top with egg slices.
Preheat oven to 400 degrees F.
Roll out dough on floured surface to 13 to 14" round.
Place atop filling.
Trim overhang to 1".
Fold overhang under and crimp edge.
Brush crust with glaze and cut slits in top of crust.
Bake for 45 minutes OR until pie is golden.
Allow to rest 15 minutes before serving.