Combine in a large bowl, or in a stand mixer, and let stand until the yeast is dissolved, about 5 minutes:
Add to the yeast mixture and mix until blended:
Gradually stir in:
Mix until the dough comes together, about 2 minutes. Knead by hand for 10 minutes or with the dough hook for about 6 minutes, until the dough is smooth and elastic and no longer sticks to your hands or the bowl. Gradually knead in:
Continue to knead until the butter is completely incorporated and the dough is soft and pliable. Place the dough in a large oiled bowl, cover with plastic wrap, and let rest in a warm place (75° to 80°F) for about 15 minutes.
Lightly oil a savarin mold or an 8-inch fluted tube or Bundt pan (oil is used because butter can pit the surface of the savarin). Gently place the dough in the mold, spreading it with your fingers so it fills the mold evenly. Cover with plastic wrap and let rise in a warm place (75° to 85°F) until doubled in volume, about 1 hour.
Preheat the oven to 350°F.
Place the pan on a baking sheet and bake until the savarin is golden brown all over, including the sides, and a knife inserted in the center comes out clean, about 45 minutes.
Immediately unmold the savarin onto a rack and let cool completely. (The savarin can be stored in a well-sealed plastic bag for up to 4 days in the refrigerator or up to 2 weeks in the freezer.)
About 15 minutes before serving, bring to a boil in a saucepan, stirring to dissolve the sugar:
Remove from the heat and stir in:
Transfer the savarin to a plate and place the plate on a rack. Place the rack on a baking sheet. Ladle the hot syrup over the top (which was the bottom as it baked) until the entire savarin is well soaked with the syrup. The syrup must be hot so the savarin can quickly absorb it without becoming soggy or losing its shape; the syrup that runs off can be rewarmed and ladled over the cake again. Let the thoroughly moistened savarin drain for about 10 minutes.
Just before serving, fill the center of the savarin with:
Top with: