Pate with Quail Egg and Chicken

Name: Pate with Quail Egg and Chicken
Ingredients: 150 grams Pastry flour; 150 grams Whole-wheat flour; 1 pinch Salt; 1 Egg; 200 grams Butter; 300 grams Chicken breast (ready to cook, skinless); 100 grams fresh Button mushrooms; 1 Shallot; 1 tablespoon Butter; 1 tablespoon Pastry flour; 100 milliliters Chicken stock; 50 milliliters dry White wine; 120 milliliters Whipping cream; freshly ground Pepper; 1 teaspoon freshly chopped Thyme; Pastry flour (for the work surface); Butter (for the ramekins); 4 colored Quail eggs