Preheat oven to 350 degrees (F). In a skillet, melt the butter and add the chopped papaya. Sprinkle with brown sugar and brandy. Saute until the papaya is very soft. Remove from heat and cool. Place in the container of a blender and puree. Crumble the butter cookies and stir into the papaya mixture. Spoon into the bottom of a 8 inch square baking pan. In a medium-sized bowl, beat the egg yolks and whole eggs until slightly thickened. Heat the milk and sugar together and bring it to a boil. Remove from heat. Pour the milk slowly into the eggs, stirring constantly until well blended. Pour over papaya in the baking pan. Cover with foil. Bake in the preheated oven for 20 to 25 minutes or until an inserted knife comes out clean.