In a small saucepan or the microwave, warm the milk to just warm, 100°F to 110°F (38°C to 43°C). Set aside.
In the bowl of a stand mixer, combine the flour, sugar, yeast, and salt. Fit the mixer with the dough hook, add the warmed milk and eggs, and mix on low speed until combined. Increase the speed to medium and let the mixer knead the dough for 5 to 10 minutes, until the dough is smooth and elastic. Add the butter 1 tablespoon at a time, then mix in the candied clementine until incorporated. Let the dough rest
for 10 minutes at room temperature.
Meanwhile, grease an eight-cavity popover pan.
Once the dough is done resting, use a 1 1/2 oz ice cream scoop to portion 3 tablespoons of dough into each cavity of the popover pan. Cover with plastic wrap and let rise in a warm place until the dough doubles in size, about 30 minutes.
Preheat the oven to 375°F (190°C). Remove from the plastic wrap and bake the babas for 15 to 20 minutes, until golden brown and an instant-read thermometer inserted in the center reads 210°F (99°C). Meanwhile, make the syrup.