Feed your starter so it's active and at its peak when you mix the dough.
Add the starter, flour, milk, water, egg, brown sugar, honey, salt and vanilla to the bowl of a stand mixer fitted with a dough hook. Mix on low until it comes together, then keep mixing for 5 to 6 minutes to start developing the gluten.
Add the soft butter a little at a time and wait for each addition to be worked in before adding the next. Once it's all in, keep mixing until the dough is smooth and passes the windowpane test, which can take another 10 to 15 minutes. If it stays greasy and won't gain strength, the butter has got too warm. Put the whole bowl in the fridge for 15 to 20 minutes, then carry on mixing.
To make this by hand, knead the dough without the butter until it passes the windowpane test, working in stages with short rests in between, then work in the butter and continue until it passes windowpane again.
Place the dough in a greased bowl or container, cover, and leave in a warm spot around 24 to 26°C (75 to 79°F) until risen by about 30 to 40%. This will take around 3 to 4 hours depending on temperature. If your kitchen is cold, use a proofing box or a turned-off oven with a mug of hot water beside the bowl, replacing the water as it cools.
Once bulked, cover tightly and refrigerate overnight.
Turn the cold dough out, weigh and divide it into 12 pieces. Shape each one into a flattish disc and place on a lined tray.
Cover and leave in a warm spot, ideally around 25°C, for about 2 hours. They should be visibly puffy but not doubled.
Preheat the waffle iron.
Working with one piece at a time, gently press the pearl sugar on, fold in thirds, add a bit more on top, and fold the two ends into the middle to make a little parcel.
Bake until deep brown and caramelised, around 3 to 4 minutes. Lift them out with silicone-tipped tongs or waffle prongs, never your fingers, and let them cool for 5 minutes before eating.
These are best served warm, either plain or dusted with icing sugar and topped with whipped cream.
Keep at room temperature for a couple of days, or freeze. Reheat in a toaster oven or air fryer.