Preheat oven to 400 F. Butter a baking dish and set aside.
On a pasta board, make a mound out of flour and make well in center, just like making fresh pasta. Place sugar, eggs and melted butter into well, using a fork, mix ingredients just like making fresh pasta. Bring dough together and knead one minute until a medium ball is formed. Divide in 4 pieces and roll each into balls. Refrigerate 15 minutes to allow to rest. Meanwhile, cut figs into halves. Remove pastry from refrigerator and roll each piece into a 4 to 5-inch circle, about 1/4-inch thick. Arrange cut fruit cut side up onto each round and bake at 400 F for about 20 to 22 minutes. Remove tarts from oven, lay 2 thin slices of Prosciutto over each, sprinkle with fennel seeds and extra virgin olive oil and serve.