In a large skillet, sauté the mushrooms in 1 tablespoon butter until tender, drain and set aside. In the same skillet, sauté the onions and beans in remaining butter for 18 - 20 minutes or until beans are crisp tender. Add the thyme, salt, pepper, cream cheese, milk and mushrooms. Cook and stir until cheese is melted. Remove from heat; set aside. In a bowl, combine the flour, baking powder, dill and salt. Cut in cold butter until mixture resembles coarse crumbs. Stir in sour cream to form soft dough. Divide dough in half. On a well floured surface, roll out one portion to fit a deep-dish 9-inch pie plate. Trim pastry even with edge. Pour green bean mixture into crust. Roll out remaining pastry; make a lattice crust. Trim, seal and flute edge. In a small bowl, beat eggs and cream. Brush over lattice top. Bake at 400° F for 25 - 35 minutes or until golden brown. Yields 8 - 10 servings.