With 2 tablespoons melted butter, coat inside of a 9-1/2-inch savarin mold. Dissolve the yeast and 1 tablespoon of the sugar in the warm water. Let sit for 2 to 5 minutes, or until foamy and showing signs of life. If the yeast is nonactive, discard and start again with new yeast. In the work bowl of a food processor combine the flour, sugar, eggs, 7 tablespoons melted butter, vanilla, and yeast mixture and process until a smooth sticky batter forms, about 1 minute. Preheat the oven to 400°. Drop the batter, 1 tablespoon at a time, into the mold, taking care not to drip batter on the sides of the mold. The mold should be filled halfway. Place a towel on the counter and bang the filled mold several times firmly on the towel to level the batter and to bring any air bubbles to the surface. Cover the mold with a large inverted bowl or pot and let rise until the batter reaches to within 1/8 inch of the top, approximately 30 minutes. Place mold on lowest rack of oven and lower the temperature to 350°. Bake 40 to 45 minutes. The cake will have risen and be dark brown on top and golden brown on bottom and sides. Unmold savarin onto a cooling rack and let cool, 20 to 30 minutes. Place the savarin, on its pastry rack, over a large bowl or deep pan. (A roasting pan or saute pan works well.) Spoon or slowly pour the boiling light sirup de sucre over the savarin and repeat until most of the syrup has been absorbed, 8 to 10 times. As the syrup cools, it should be reheated. When there is only about 1/2 cup of syrup remaining, stop and slowly spoon the rum over the savarin. Follow the rum with the remaining syrup. In a small saucepan bring the glacage a labricot to a boil over medium heat. Using a pastry brush, coat the entire savarin with a layer of the glaze. Decorate as desired. Using two long metal spatulas, transfer the savarin to a large rimmed serving platter. Pour any remaining syrup around the savarin.