Melt the butter in a saucepan, stir in the flour, and cook 2 minutes
over
low heat. Remove from the heat and stir in the milk and the broth;
return
to heat and stir the mixture until it is thick and smooth. In
a greased
casserole, put the turkey and ham, evenly distributed, then pour
in half
the sauce; keep the remainder hot. Top the contents of the casserole
with
bread crumbs and the cheeses.
Bake in a preheated 350F oven until
a
crusty, lightly brown surface develops, about 25 minutes. Make
4
indentations on the surface and carefully break an egg into each,
cover
them with the remaining hot sauce, and return to the oven for
about 18
minutes, until the eggs have set.