For batter: Place flour in bowl. Gradually add eggs and milk, beating continuously. Season with salt and pepper. Set aside in a cool place for 4 hours.
For filling: Melt butter in saucepan over moderate heat. Gradually add in flour and cook 3 minutes, stirring constantly. Add chicken stock, whisking continuously until thoroughly blended. Bring to boil and cook 3 minutes. Reduce heat to gentle simmer.
In frying pan, cook chicken in a little clarified butter over moderate heat. Rub tarragon between palms over chicken to coarsely grind. Season with salt and white pepper. After 4 minutes, turn breasts over, reduce heat and cook until done.
To assemble: Meanwhile, preheat broiler. Melt 2 tablespoons butter in omelet pan. Pour butter into pancake batter and mix well. Pour a good amount of pancake batter into pan to make heavy pancakes. When one side is cooked, do not flip. Add 2 tablespoons grated cheese to uncooked side and place under broiler for a moment to brown. Repeat to make 1 more pancake.
Lay 1 chicken breast on the cheese side of each pancake. Cover chicken with prosciutto and fold pancake over to form a semi-circle.
To hot sauce, add 2 tablespoons cheese and pour over pancakes. Sprinkle tops of pancakes with remaining cheese and broil for 2 minutes. To serve, sprinkle with chives and garnish with caviar.