To make the baba, mix the yeast, sugar, salt, and eggs together. Add the flour and cooled butter. (The dough will be very sticky.) Stir vigorously with a large wooden spoon or with your hands until the dough becomes smooth and elastic. Place in a large, buttered bowl. Cut a deep X into the top of the dough and sprinkle with a bit of extra flour. Cover and let rise in a warm place until doubled in bulk, about 1 hour.
Butter a 9 inch ring mold. Punch down the dough and knead until smooth on a lightly floured board. Form into a ring large enough to fit the pan. Let the dough rise in the pan, uncovered, until it has reached the top of the mold. Do not let rise too much or it will collapse during baking. Preheat the oven to 375F.
Bake the baba about 30 minutes, or until golden in color and shrinking from the sides of the pan. Remove from the oven, cool for 5 minutes in the pan, then turn out onto the rack and cool just until the baba is warm before soaking.
To Make The Rum Syrup: Boil the sugar and water until dissolved. Add the rum and cool to tepid.
Pierce the puffed top of the baba all over with a fork. Place puffed side down in a shallow dish and baste the entire cake with rum syrup. The baba should be moist but not soggy. Pour off excess syrup.
To Make The Glaze: Strain the jam and melt with the rum. Brush the top of the baba with the mixture, and decorate with glaceed cherries.