In a large mixing bowl combine water, yeast, and sugar. Let sit for 10 minutes until foamy. You want to make sure the water is at around 110°F so that it’s warm enough for the yeast to activate but not so hot it kills it. It should look foamy when ready.
Add in the salt, rosemary, egg, and milk, and mix to combine with a wooden spoon.
Add in the first addition of flour, 90 grams (about 3/4 cup) and mix to combine.
Add in the butter, and mix until incorporated. No worries if there are few bits.
Add in the 110 grams (3/4 cup and 2 tablespoons) flour, and mix until dough comes together.
Turn dough out onto a floured work surface. The dough will be very sticky. And annoying. You haven’t messed up. Knead in the remaining 1/4 cup of flour by hand until dough is smooth, a couple of minutes.
Form dough into a ball and put in a clean, lightly oiled bowl loosely covered with plastic wrap or covered with a (non-terry cloth) dish towel.
Let stand in a warm area until doubled in size, about 2-3 hours.
Remove dough from bowl onto a well floured work surface and lightly dust top with flour.
Heat 1.5-2 inches of canola oil in a cast iron (preferably) pan to 350°f.
Meanwhile, roll out dough to 1/2 inch thick.
Cut out 2.5” round circles of dough with a biscuit cutter, re-rolling and cutting until all the dough has been used. Gently press a truffle into the center of each, and wrap the dough around it, pinching to seal very well. You don’t want any molten chocolate seeping out.
Set a cooling rack over a paper towel lined baking sheet.
Using a slotted metal spatula or spoon gently transfer the beignets to the hot oil and fry 3-4 at a time, rolling them around frequently, until golden brown on all sides. this takes about 3-4 minutes.
As they finish transfer them to the cooling rack over paper towels.
Dust liberally with powdered sugar and serve warm.
Repeat with all remaining donuts. While they’re optimal served fresh, you can store them, covered at room temperature. I don’t like to do this and try to eat/give them away while warm; they make fantastic party food.