In a medium bowl, stir the lukewarm water with the sugar and yeast. Wait until you see tiny bubbles forming (this is proofing the yeast and takes about 5 minutes).
To the yeast mixture, add the egg, salt, and half-and-half. Stir, then add the flour and 1 tablespoon coconut oil. Stir well to form a very sticky dough.
Dust the counter with flour and knead the dough for several minutes, adding a bit of flour only if necessary, until the surface becomes smooth, about 5 minutes. Grease a bowl and set the dough inside. Cover with plastic wrap and let rise in a warm place until doubled in size, about 2 hours.
Preheat the refined coconut oil in a dedicated fryer or Dutch oven over medium heat to 365°F.
Roll the dough into a rectangular shape approximately ¼-inch thick; cut into rows, then rectangles forming about 24 little rectangles. Fry 5 to 6 pieces of dough at a time, turning constantly until golden with a spider, tongs, or slotted spoon. Transfer to a plate lined with paper towels.
Fill a piping bag with nutella; poke a hole in each beignet using the metal tip and squeeze to fill each donut with nutella. Dust the beignets with powdered sugar (and cinnamon, optional) and enjoy with coffee, if desired.
