The day before, prepare the kumquats: wash, pat dry, slice into 3 mm pieces, and remove the seeds. Place in a bowl with 100 g sugar, mix, and let macerate overnight.
Prepare the dough: Pour 10 cl lukewarm water into a glass, add the yeast, and let activate for 8-10 minutes. In a mixing bowl, combine flour, salt, 10 g sugar, and the yeast mixture. Blend for 30 seconds, adding eggs one by one. Knead for 10 minutes, then incorporate the butter and knead another 3 minutes for a smooth dough.
Grease 12 small baba molds and divide the dough evenly. Let rise at room temperature until doubled, about 15-20 minutes.
Preheat oven to 210°C (thermostat 7). Bake babas for 25-30 minutes until golden brown.
Make the syrup: In a saucepan, combine remaining 300 g sugar with 30 cl water. Bring to a boil and simmer 5 minutes. Remove from heat, stir in rum, add macerated kumquats and their juice.
Dip warm babas in hot syrup for 30 seconds, then drain on a serving platter. Arrange kumquat slices on top. Cool before serving.
