Butter, then flour, a 12-cup muffin pan, and set aside.
In a small mixing bowl, stir together the yeast and warm water until the yeast dissolves.
Add 1/8 cup flour, stirring until a paste is formed. Set aside for 10 minutes.
In a mixing bowl, beat the butter and sugar together with an electric mixer for about 5 to 6 minutes, until a light ribbon is formed.
Remove the beaters and clean all of the butter mixture off the beaters into the bowl.
Place a dough hook attachment on the mixer and add the yeast mixture, the remaining flour, the salt, the eggs and yolks and mix well, about 8 to 9 minutes, until the dough pulls away from the sides of the bowl.
Remove the dough from the mixing bowl and divide it into 12 equal portions.
Place each portion into a cup of the prepared muffin pan, cover with a towel and allow to stand for 1 hour, to double in bulk.
Place the cakes in the oven and bake for 20 to 25 minutes, until cooked through or when a toothpick entered at the center exits clean.
Remove and allow to cool on a cake rack for 20 minutes.
Remove the cakes from the pan and place them on a sheet tray.
In a small saucepan, heat the water and sugar to boiling and stir to dissolve the sugar. Lower heat to a very high simmer and cook 15 minutes to form a simple syrup.
Remove from heat, add rum, stir to mix and allow to cool 5 minutes.
Poke the tops of the cakes with a popsicle stick to form 8 to 10 slender holes. Spoon the rum syrup over the cakes and into the holes, and repeat twice with the syrup that drains out of the bottom.
